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cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/__init__.py
|
"Iterative Solvers for Sparse Linear Systems"
from __future__ import division, print_function, absolute_import
#from info import __doc__
from .iterative import *
from .minres import minres
from .lgmres import lgmres
from .lsqr import lsqr
from .lsmr import lsmr
from ._gcrotmk import gcrotmk
__all__ = [s for s in dir() if not s.startswith('_')]
from scipy._lib._testutils import PytestTester
test = PytestTester(__name__)
del PytestTester
| 444 | 23.722222 | 64 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/lsmr.py
|
"""
Copyright (C) 2010 David Fong and Michael Saunders
LSMR uses an iterative method.
07 Jun 2010: Documentation updated
03 Jun 2010: First release version in Python
David Chin-lung Fong clfong@stanford.edu
Institute for Computational and Mathematical Engineering
Stanford University
Michael Saunders saunders@stanford.edu
Systems Optimization Laboratory
Dept of MS&E, Stanford University.
"""
from __future__ import division, print_function, absolute_import
__all__ = ['lsmr']
from numpy import zeros, infty, atleast_1d
from numpy.linalg import norm
from math import sqrt
from scipy.sparse.linalg.interface import aslinearoperator
from .lsqr import _sym_ortho
def lsmr(A, b, damp=0.0, atol=1e-6, btol=1e-6, conlim=1e8,
maxiter=None, show=False, x0=None):
"""Iterative solver for least-squares problems.
lsmr solves the system of linear equations ``Ax = b``. If the system
is inconsistent, it solves the least-squares problem ``min ||b - Ax||_2``.
A is a rectangular matrix of dimension m-by-n, where all cases are
allowed: m = n, m > n, or m < n. B is a vector of length m.
The matrix A may be dense or sparse (usually sparse).
Parameters
----------
A : {matrix, sparse matrix, ndarray, LinearOperator}
Matrix A in the linear system.
b : array_like, shape (m,)
Vector b in the linear system.
damp : float
Damping factor for regularized least-squares. `lsmr` solves
the regularized least-squares problem::
min ||(b) - ( A )x||
||(0) (damp*I) ||_2
where damp is a scalar. If damp is None or 0, the system
is solved without regularization.
atol, btol : float, optional
Stopping tolerances. `lsmr` continues iterations until a
certain backward error estimate is smaller than some quantity
depending on atol and btol. Let ``r = b - Ax`` be the
residual vector for the current approximate solution ``x``.
If ``Ax = b`` seems to be consistent, ``lsmr`` terminates
when ``norm(r) <= atol * norm(A) * norm(x) + btol * norm(b)``.
Otherwise, lsmr terminates when ``norm(A^{T} r) <=
atol * norm(A) * norm(r)``. If both tolerances are 1.0e-6 (say),
the final ``norm(r)`` should be accurate to about 6
digits. (The final x will usually have fewer correct digits,
depending on ``cond(A)`` and the size of LAMBDA.) If `atol`
or `btol` is None, a default value of 1.0e-6 will be used.
Ideally, they should be estimates of the relative error in the
entries of A and B respectively. For example, if the entries
of `A` have 7 correct digits, set atol = 1e-7. This prevents
the algorithm from doing unnecessary work beyond the
uncertainty of the input data.
conlim : float, optional
`lsmr` terminates if an estimate of ``cond(A)`` exceeds
`conlim`. For compatible systems ``Ax = b``, conlim could be
as large as 1.0e+12 (say). For least-squares problems,
`conlim` should be less than 1.0e+8. If `conlim` is None, the
default value is 1e+8. Maximum precision can be obtained by
setting ``atol = btol = conlim = 0``, but the number of
iterations may then be excessive.
maxiter : int, optional
`lsmr` terminates if the number of iterations reaches
`maxiter`. The default is ``maxiter = min(m, n)``. For
ill-conditioned systems, a larger value of `maxiter` may be
needed.
show : bool, optional
Print iterations logs if ``show=True``.
x0 : array_like, shape (n,), optional
Initial guess of x, if None zeros are used.
.. versionadded:: 1.0.0
Returns
-------
x : ndarray of float
Least-square solution returned.
istop : int
istop gives the reason for stopping::
istop = 0 means x=0 is a solution. If x0 was given, then x=x0 is a
solution.
= 1 means x is an approximate solution to A*x = B,
according to atol and btol.
= 2 means x approximately solves the least-squares problem
according to atol.
= 3 means COND(A) seems to be greater than CONLIM.
= 4 is the same as 1 with atol = btol = eps (machine
precision)
= 5 is the same as 2 with atol = eps.
= 6 is the same as 3 with CONLIM = 1/eps.
= 7 means ITN reached maxiter before the other stopping
conditions were satisfied.
itn : int
Number of iterations used.
normr : float
``norm(b-Ax)``
normar : float
``norm(A^T (b - Ax))``
norma : float
``norm(A)``
conda : float
Condition number of A.
normx : float
``norm(x)``
Notes
-----
.. versionadded:: 0.11.0
References
----------
.. [1] D. C.-L. Fong and M. A. Saunders,
"LSMR: An iterative algorithm for sparse least-squares problems",
SIAM J. Sci. Comput., vol. 33, pp. 2950-2971, 2011.
http://arxiv.org/abs/1006.0758
.. [2] LSMR Software, http://web.stanford.edu/group/SOL/software/lsmr/
Examples
--------
>>> from scipy.sparse import csc_matrix
>>> from scipy.sparse.linalg import lsmr
>>> A = csc_matrix([[1., 0.], [1., 1.], [0., 1.]], dtype=float)
The first example has the trivial solution `[0, 0]`
>>> b = np.array([0., 0., 0.], dtype=float)
>>> x, istop, itn, normr = lsmr(A, b)[:4]
>>> istop
0
>>> x
array([ 0., 0.])
The stopping code `istop=0` returned indicates that a vector of zeros was
found as a solution. The returned solution `x` indeed contains `[0., 0.]`.
The next example has a non-trivial solution:
>>> b = np.array([1., 0., -1.], dtype=float)
>>> x, istop, itn, normr = lsmr(A, b)[:4]
>>> istop
1
>>> x
array([ 1., -1.])
>>> itn
1
>>> normr
4.440892098500627e-16
As indicated by `istop=1`, `lsmr` found a solution obeying the tolerance
limits. The given solution `[1., -1.]` obviously solves the equation. The
remaining return values include information about the number of iterations
(`itn=1`) and the remaining difference of left and right side of the solved
equation.
The final example demonstrates the behavior in the case where there is no
solution for the equation:
>>> b = np.array([1., 0.01, -1.], dtype=float)
>>> x, istop, itn, normr = lsmr(A, b)[:4]
>>> istop
2
>>> x
array([ 1.00333333, -0.99666667])
>>> A.dot(x)-b
array([ 0.00333333, -0.00333333, 0.00333333])
>>> normr
0.005773502691896255
`istop` indicates that the system is inconsistent and thus `x` is rather an
approximate solution to the corresponding least-squares problem. `normr`
contains the minimal distance that was found.
"""
A = aslinearoperator(A)
b = atleast_1d(b)
if b.ndim > 1:
b = b.squeeze()
msg = ('The exact solution is x = 0, or x = x0, if x0 was given ',
'Ax - b is small enough, given atol, btol ',
'The least-squares solution is good enough, given atol ',
'The estimate of cond(Abar) has exceeded conlim ',
'Ax - b is small enough for this machine ',
'The least-squares solution is good enough for this machine',
'Cond(Abar) seems to be too large for this machine ',
'The iteration limit has been reached ')
hdg1 = ' itn x(1) norm r norm A''r'
hdg2 = ' compatible LS norm A cond A'
pfreq = 20 # print frequency (for repeating the heading)
pcount = 0 # print counter
m, n = A.shape
# stores the num of singular values
minDim = min([m, n])
if maxiter is None:
maxiter = minDim
if show:
print(' ')
print('LSMR Least-squares solution of Ax = b\n')
print('The matrix A has %8g rows and %8g cols' % (m, n))
print('damp = %20.14e\n' % (damp))
print('atol = %8.2e conlim = %8.2e\n' % (atol, conlim))
print('btol = %8.2e maxiter = %8g\n' % (btol, maxiter))
u = b
normb = norm(b)
if x0 is None:
x = zeros(n)
beta = normb.copy()
else:
x = atleast_1d(x0)
u = u - A.matvec(x)
beta = norm(u)
if beta > 0:
u = (1 / beta) * u
v = A.rmatvec(u)
alpha = norm(v)
else:
v = zeros(n)
alpha = 0
if alpha > 0:
v = (1 / alpha) * v
# Initialize variables for 1st iteration.
itn = 0
zetabar = alpha * beta
alphabar = alpha
rho = 1
rhobar = 1
cbar = 1
sbar = 0
h = v.copy()
hbar = zeros(n)
# Initialize variables for estimation of ||r||.
betadd = beta
betad = 0
rhodold = 1
tautildeold = 0
thetatilde = 0
zeta = 0
d = 0
# Initialize variables for estimation of ||A|| and cond(A)
normA2 = alpha * alpha
maxrbar = 0
minrbar = 1e+100
normA = sqrt(normA2)
condA = 1
normx = 0
# Items for use in stopping rules, normb set earlier
istop = 0
ctol = 0
if conlim > 0:
ctol = 1 / conlim
normr = beta
# Reverse the order here from the original matlab code because
# there was an error on return when arnorm==0
normar = alpha * beta
if normar == 0:
if show:
print(msg[0])
return x, istop, itn, normr, normar, normA, condA, normx
if show:
print(' ')
print(hdg1, hdg2)
test1 = 1
test2 = alpha / beta
str1 = '%6g %12.5e' % (itn, x[0])
str2 = ' %10.3e %10.3e' % (normr, normar)
str3 = ' %8.1e %8.1e' % (test1, test2)
print(''.join([str1, str2, str3]))
# Main iteration loop.
while itn < maxiter:
itn = itn + 1
# Perform the next step of the bidiagonalization to obtain the
# next beta, u, alpha, v. These satisfy the relations
# beta*u = a*v - alpha*u,
# alpha*v = A'*u - beta*v.
u = A.matvec(v) - alpha * u
beta = norm(u)
if beta > 0:
u = (1 / beta) * u
v = A.rmatvec(u) - beta * v
alpha = norm(v)
if alpha > 0:
v = (1 / alpha) * v
# At this point, beta = beta_{k+1}, alpha = alpha_{k+1}.
# Construct rotation Qhat_{k,2k+1}.
chat, shat, alphahat = _sym_ortho(alphabar, damp)
# Use a plane rotation (Q_i) to turn B_i to R_i
rhoold = rho
c, s, rho = _sym_ortho(alphahat, beta)
thetanew = s*alpha
alphabar = c*alpha
# Use a plane rotation (Qbar_i) to turn R_i^T to R_i^bar
rhobarold = rhobar
zetaold = zeta
thetabar = sbar * rho
rhotemp = cbar * rho
cbar, sbar, rhobar = _sym_ortho(cbar * rho, thetanew)
zeta = cbar * zetabar
zetabar = - sbar * zetabar
# Update h, h_hat, x.
hbar = h - (thetabar * rho / (rhoold * rhobarold)) * hbar
x = x + (zeta / (rho * rhobar)) * hbar
h = v - (thetanew / rho) * h
# Estimate of ||r||.
# Apply rotation Qhat_{k,2k+1}.
betaacute = chat * betadd
betacheck = -shat * betadd
# Apply rotation Q_{k,k+1}.
betahat = c * betaacute
betadd = -s * betaacute
# Apply rotation Qtilde_{k-1}.
# betad = betad_{k-1} here.
thetatildeold = thetatilde
ctildeold, stildeold, rhotildeold = _sym_ortho(rhodold, thetabar)
thetatilde = stildeold * rhobar
rhodold = ctildeold * rhobar
betad = - stildeold * betad + ctildeold * betahat
# betad = betad_k here.
# rhodold = rhod_k here.
tautildeold = (zetaold - thetatildeold * tautildeold) / rhotildeold
taud = (zeta - thetatilde * tautildeold) / rhodold
d = d + betacheck * betacheck
normr = sqrt(d + (betad - taud)**2 + betadd * betadd)
# Estimate ||A||.
normA2 = normA2 + beta * beta
normA = sqrt(normA2)
normA2 = normA2 + alpha * alpha
# Estimate cond(A).
maxrbar = max(maxrbar, rhobarold)
if itn > 1:
minrbar = min(minrbar, rhobarold)
condA = max(maxrbar, rhotemp) / min(minrbar, rhotemp)
# Test for convergence.
# Compute norms for convergence testing.
normar = abs(zetabar)
normx = norm(x)
# Now use these norms to estimate certain other quantities,
# some of which will be small near a solution.
test1 = normr / normb
if (normA * normr) != 0:
test2 = normar / (normA * normr)
else:
test2 = infty
test3 = 1 / condA
t1 = test1 / (1 + normA * normx / normb)
rtol = btol + atol * normA * normx / normb
# The following tests guard against extremely small values of
# atol, btol or ctol. (The user may have set any or all of
# the parameters atol, btol, conlim to 0.)
# The effect is equivalent to the normAl tests using
# atol = eps, btol = eps, conlim = 1/eps.
if itn >= maxiter:
istop = 7
if 1 + test3 <= 1:
istop = 6
if 1 + test2 <= 1:
istop = 5
if 1 + t1 <= 1:
istop = 4
# Allow for tolerances set by the user.
if test3 <= ctol:
istop = 3
if test2 <= atol:
istop = 2
if test1 <= rtol:
istop = 1
# See if it is time to print something.
if show:
if (n <= 40) or (itn <= 10) or (itn >= maxiter - 10) or \
(itn % 10 == 0) or (test3 <= 1.1 * ctol) or \
(test2 <= 1.1 * atol) or (test1 <= 1.1 * rtol) or \
(istop != 0):
if pcount >= pfreq:
pcount = 0
print(' ')
print(hdg1, hdg2)
pcount = pcount + 1
str1 = '%6g %12.5e' % (itn, x[0])
str2 = ' %10.3e %10.3e' % (normr, normar)
str3 = ' %8.1e %8.1e' % (test1, test2)
str4 = ' %8.1e %8.1e' % (normA, condA)
print(''.join([str1, str2, str3, str4]))
if istop > 0:
break
# Print the stopping condition.
if show:
print(' ')
print('LSMR finished')
print(msg[istop])
print('istop =%8g normr =%8.1e' % (istop, normr))
print(' normA =%8.1e normAr =%8.1e' % (normA, normar))
print('itn =%8g condA =%8.1e' % (itn, condA))
print(' normx =%8.1e' % (normx))
print(str1, str2)
print(str3, str4)
return x, istop, itn, normr, normar, normA, condA, normx
| 15,126 | 31.116773 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/_gcrotmk.py
|
# Copyright (C) 2015, Pauli Virtanen <pav@iki.fi>
# Distributed under the same license as Scipy.
from __future__ import division, print_function, absolute_import
import warnings
import numpy as np
from numpy.linalg import LinAlgError
from scipy._lib.six import xrange
from scipy.linalg import (get_blas_funcs, qr, solve, svd, qr_insert, lstsq)
from scipy.sparse.linalg.isolve.utils import make_system
__all__ = ['gcrotmk']
def _fgmres(matvec, v0, m, atol, lpsolve=None, rpsolve=None, cs=(), outer_v=(),
prepend_outer_v=False):
"""
FGMRES Arnoldi process, with optional projection or augmentation
Parameters
----------
matvec : callable
Operation A*x
v0 : ndarray
Initial vector, normalized to nrm2(v0) == 1
m : int
Number of GMRES rounds
atol : float
Absolute tolerance for early exit
lpsolve : callable
Left preconditioner L
rpsolve : callable
Right preconditioner R
CU : list of (ndarray, ndarray)
Columns of matrices C and U in GCROT
outer_v : list of ndarrays
Augmentation vectors in LGMRES
prepend_outer_v : bool, optional
Whether augmentation vectors come before or after
Krylov iterates
Raises
------
LinAlgError
If nans encountered
Returns
-------
Q, R : ndarray
QR decomposition of the upper Hessenberg H=QR
B : ndarray
Projections corresponding to matrix C
vs : list of ndarray
Columns of matrix V
zs : list of ndarray
Columns of matrix Z
y : ndarray
Solution to ||H y - e_1||_2 = min!
res : float
The final (preconditioned) residual norm
"""
if lpsolve is None:
lpsolve = lambda x: x
if rpsolve is None:
rpsolve = lambda x: x
axpy, dot, scal, nrm2 = get_blas_funcs(['axpy', 'dot', 'scal', 'nrm2'], (v0,))
vs = [v0]
zs = []
y = None
res = np.nan
m = m + len(outer_v)
# Orthogonal projection coefficients
B = np.zeros((len(cs), m), dtype=v0.dtype)
# H is stored in QR factorized form
Q = np.ones((1, 1), dtype=v0.dtype)
R = np.zeros((1, 0), dtype=v0.dtype)
eps = np.finfo(v0.dtype).eps
breakdown = False
# FGMRES Arnoldi process
for j in xrange(m):
# L A Z = C B + V H
if prepend_outer_v and j < len(outer_v):
z, w = outer_v[j]
elif prepend_outer_v and j == len(outer_v):
z = rpsolve(v0)
w = None
elif not prepend_outer_v and j >= m - len(outer_v):
z, w = outer_v[j - (m - len(outer_v))]
else:
z = rpsolve(vs[-1])
w = None
if w is None:
w = lpsolve(matvec(z))
else:
# w is clobbered below
w = w.copy()
w_norm = nrm2(w)
# GCROT projection: L A -> (1 - C C^H) L A
# i.e. orthogonalize against C
for i, c in enumerate(cs):
alpha = dot(c, w)
B[i,j] = alpha
w = axpy(c, w, c.shape[0], -alpha) # w -= alpha*c
# Orthogonalize against V
hcur = np.zeros(j+2, dtype=Q.dtype)
for i, v in enumerate(vs):
alpha = dot(v, w)
hcur[i] = alpha
w = axpy(v, w, v.shape[0], -alpha) # w -= alpha*v
hcur[i+1] = nrm2(w)
with np.errstate(over='ignore', divide='ignore'):
# Careful with denormals
alpha = 1/hcur[-1]
if np.isfinite(alpha):
w = scal(alpha, w)
if not (hcur[-1] > eps * w_norm):
# w essentially in the span of previous vectors,
# or we have nans. Bail out after updating the QR
# solution.
breakdown = True
vs.append(w)
zs.append(z)
# Arnoldi LSQ problem
# Add new column to H=Q*R, padding other columns with zeros
Q2 = np.zeros((j+2, j+2), dtype=Q.dtype, order='F')
Q2[:j+1,:j+1] = Q
Q2[j+1,j+1] = 1
R2 = np.zeros((j+2, j), dtype=R.dtype, order='F')
R2[:j+1,:] = R
Q, R = qr_insert(Q2, R2, hcur, j, which='col',
overwrite_qru=True, check_finite=False)
# Transformed least squares problem
# || Q R y - inner_res_0 * e_1 ||_2 = min!
# Since R = [R'; 0], solution is y = inner_res_0 (R')^{-1} (Q^H)[:j,0]
# Residual is immediately known
res = abs(Q[0,-1])
# Check for termination
if res < atol or breakdown:
break
if not np.isfinite(R[j,j]):
# nans encountered, bail out
raise LinAlgError()
# -- Get the LSQ problem solution
# The problem is triangular, but the condition number may be
# bad (or in case of breakdown the last diagonal entry may be
# zero), so use lstsq instead of trtrs.
y, _, _, _, = lstsq(R[:j+1,:j+1], Q[0,:j+1].conj())
B = B[:,:j+1]
return Q, R, B, vs, zs, y, res
def gcrotmk(A, b, x0=None, tol=1e-5, maxiter=1000, M=None, callback=None,
m=20, k=None, CU=None, discard_C=False, truncate='oldest',
atol=None):
"""
Solve a matrix equation using flexible GCROT(m,k) algorithm.
Parameters
----------
A : {sparse matrix, dense matrix, LinearOperator}
The real or complex N-by-N matrix of the linear system.
b : {array, matrix}
Right hand side of the linear system. Has shape (N,) or (N,1).
x0 : {array, matrix}
Starting guess for the solution.
tol, atol : float, optional
Tolerances for convergence, ``norm(residual) <= max(tol*norm(b), atol)``.
The default for ``atol`` is `tol`.
.. warning::
The default value for `atol` will be changed in a future release.
For future compatibility, specify `atol` explicitly.
maxiter : int, optional
Maximum number of iterations. Iteration will stop after maxiter
steps even if the specified tolerance has not been achieved.
M : {sparse matrix, dense matrix, LinearOperator}, optional
Preconditioner for A. The preconditioner should approximate the
inverse of A. gcrotmk is a 'flexible' algorithm and the preconditioner
can vary from iteration to iteration. Effective preconditioning
dramatically improves the rate of convergence, which implies that
fewer iterations are needed to reach a given error tolerance.
callback : function, optional
User-supplied function to call after each iteration. It is called
as callback(xk), where xk is the current solution vector.
m : int, optional
Number of inner FGMRES iterations per each outer iteration.
Default: 20
k : int, optional
Number of vectors to carry between inner FGMRES iterations.
According to [2]_, good values are around m.
Default: m
CU : list of tuples, optional
List of tuples ``(c, u)`` which contain the columns of the matrices
C and U in the GCROT(m,k) algorithm. For details, see [2]_.
The list given and vectors contained in it are modified in-place.
If not given, start from empty matrices. The ``c`` elements in the
tuples can be ``None``, in which case the vectors are recomputed
via ``c = A u`` on start and orthogonalized as described in [3]_.
discard_C : bool, optional
Discard the C-vectors at the end. Useful if recycling Krylov subspaces
for different linear systems.
truncate : {'oldest', 'smallest'}, optional
Truncation scheme to use. Drop: oldest vectors, or vectors with
smallest singular values using the scheme discussed in [1,2].
See [2]_ for detailed comparison.
Default: 'oldest'
Returns
-------
x : array or matrix
The solution found.
info : int
Provides convergence information:
* 0 : successful exit
* >0 : convergence to tolerance not achieved, number of iterations
References
----------
.. [1] E. de Sturler, ''Truncation strategies for optimal Krylov subspace
methods'', SIAM J. Numer. Anal. 36, 864 (1999).
.. [2] J.E. Hicken and D.W. Zingg, ''A simplified and flexible variant
of GCROT for solving nonsymmetric linear systems'',
SIAM J. Sci. Comput. 32, 172 (2010).
.. [3] M.L. Parks, E. de Sturler, G. Mackey, D.D. Johnson, S. Maiti,
''Recycling Krylov subspaces for sequences of linear systems'',
SIAM J. Sci. Comput. 28, 1651 (2006).
"""
A,M,x,b,postprocess = make_system(A,M,x0,b)
if not np.isfinite(b).all():
raise ValueError("RHS must contain only finite numbers")
if truncate not in ('oldest', 'smallest'):
raise ValueError("Invalid value for 'truncate': %r" % (truncate,))
if atol is None:
warnings.warn("scipy.sparse.linalg.gcrotmk called without specifying `atol`. "
"The default value will change in the future. To preserve "
"current behavior, set ``atol=tol``.",
category=DeprecationWarning, stacklevel=2)
atol = tol
matvec = A.matvec
psolve = M.matvec
if CU is None:
CU = []
if k is None:
k = m
axpy, dot, scal = None, None, None
r = b - matvec(x)
axpy, dot, scal, nrm2 = get_blas_funcs(['axpy', 'dot', 'scal', 'nrm2'], (x, r))
b_norm = nrm2(b)
if discard_C:
CU[:] = [(None, u) for c, u in CU]
# Reorthogonalize old vectors
if CU:
# Sort already existing vectors to the front
CU.sort(key=lambda cu: cu[0] is not None)
# Fill-in missing ones
C = np.empty((A.shape[0], len(CU)), dtype=r.dtype, order='F')
us = []
j = 0
while CU:
# More memory-efficient: throw away old vectors as we go
c, u = CU.pop(0)
if c is None:
c = matvec(u)
C[:,j] = c
j += 1
us.append(u)
# Orthogonalize
Q, R, P = qr(C, overwrite_a=True, mode='economic', pivoting=True)
del C
# C := Q
cs = list(Q.T)
# U := U P R^-1, back-substitution
new_us = []
for j in xrange(len(cs)):
u = us[P[j]]
for i in xrange(j):
u = axpy(us[P[i]], u, u.shape[0], -R[i,j])
if abs(R[j,j]) < 1e-12 * abs(R[0,0]):
# discard rest of the vectors
break
u = scal(1.0/R[j,j], u)
new_us.append(u)
# Form the new CU lists
CU[:] = list(zip(cs, new_us))[::-1]
if CU:
axpy, dot = get_blas_funcs(['axpy', 'dot'], (r,))
# Solve first the projection operation with respect to the CU
# vectors. This corresponds to modifying the initial guess to
# be
#
# x' = x + U y
# y = argmin_y || b - A (x + U y) ||^2
#
# The solution is y = C^H (b - A x)
for c, u in CU:
yc = dot(c, r)
x = axpy(u, x, x.shape[0], yc)
r = axpy(c, r, r.shape[0], -yc)
# GCROT main iteration
for j_outer in xrange(maxiter):
# -- callback
if callback is not None:
callback(x)
beta = nrm2(r)
# -- check stopping condition
beta_tol = max(atol, tol * b_norm)
if beta <= beta_tol and (j_outer > 0 or CU):
# recompute residual to avoid rounding error
r = b - matvec(x)
beta = nrm2(r)
if beta <= beta_tol:
j_outer = -1
break
ml = m + max(k - len(CU), 0)
cs = [c for c, u in CU]
try:
Q, R, B, vs, zs, y, pres = _fgmres(matvec,
r/beta,
ml,
rpsolve=psolve,
atol=max(atol, tol*b_norm)/beta,
cs=cs)
y *= beta
except LinAlgError:
# Floating point over/underflow, non-finite result from
# matmul etc. -- report failure.
break
#
# At this point,
#
# [A U, A Z] = [C, V] G; G = [ I B ]
# [ 0 H ]
#
# where [C, V] has orthonormal columns, and r = beta v_0. Moreover,
#
# || b - A (x + Z y + U q) ||_2 = || r - C B y - V H y - C q ||_2 = min!
#
# from which y = argmin_y || beta e_1 - H y ||_2, and q = -B y
#
#
# GCROT(m,k) update
#
# Define new outer vectors
# ux := (Z - U B) y
ux = zs[0]*y[0]
for z, yc in zip(zs[1:], y[1:]):
ux = axpy(z, ux, ux.shape[0], yc) # ux += z*yc
by = B.dot(y)
for cu, byc in zip(CU, by):
c, u = cu
ux = axpy(u, ux, ux.shape[0], -byc) # ux -= u*byc
# cx := V H y
hy = Q.dot(R.dot(y))
cx = vs[0] * hy[0]
for v, hyc in zip(vs[1:], hy[1:]):
cx = axpy(v, cx, cx.shape[0], hyc) # cx += v*hyc
# Normalize cx, maintaining cx = A ux
# This new cx is orthogonal to the previous C, by construction
try:
alpha = 1/nrm2(cx)
if not np.isfinite(alpha):
raise FloatingPointError()
except (FloatingPointError, ZeroDivisionError):
# Cannot update, so skip it
continue
cx = scal(alpha, cx)
ux = scal(alpha, ux)
# Update residual and solution
gamma = dot(cx, r)
r = axpy(cx, r, r.shape[0], -gamma) # r -= gamma*cx
x = axpy(ux, x, x.shape[0], gamma) # x += gamma*ux
# Truncate CU
if truncate == 'oldest':
while len(CU) >= k and CU:
del CU[0]
elif truncate == 'smallest':
if len(CU) >= k and CU:
# cf. [1,2]
D = solve(R[:-1,:].T, B.T).T
W, sigma, V = svd(D)
# C := C W[:,:k-1], U := U W[:,:k-1]
new_CU = []
for j, w in enumerate(W[:,:k-1].T):
c, u = CU[0]
c = c * w[0]
u = u * w[0]
for cup, wp in zip(CU[1:], w[1:]):
cp, up = cup
c = axpy(cp, c, c.shape[0], wp)
u = axpy(up, u, u.shape[0], wp)
# Reorthogonalize at the same time; not necessary
# in exact arithmetic, but floating point error
# tends to accumulate here
for cp, up in new_CU:
alpha = dot(cp, c)
c = axpy(cp, c, c.shape[0], -alpha)
u = axpy(up, u, u.shape[0], -alpha)
alpha = nrm2(c)
c = scal(1.0/alpha, c)
u = scal(1.0/alpha, u)
new_CU.append((c, u))
CU[:] = new_CU
# Add new vector to CU
CU.append((cx, ux))
# Include the solution vector to the span
CU.append((None, x.copy()))
if discard_C:
CU[:] = [(None, uz) for cz, uz in CU]
return postprocess(x), j_outer + 1
| 15,478 | 30.719262 | 86 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/test_gcrotmk.py
|
#!/usr/bin/env python
"""Tests for the linalg.isolve.gcrotmk module
"""
from __future__ import division, print_function, absolute_import
from numpy.testing import assert_, assert_allclose, assert_equal
from scipy._lib._numpy_compat import suppress_warnings
import numpy as np
from numpy import zeros, array, allclose
from scipy.linalg import norm
from scipy.sparse import csr_matrix, eye, rand
from scipy.sparse.linalg.interface import LinearOperator
from scipy.sparse.linalg import splu
from scipy.sparse.linalg.isolve import gcrotmk, gmres
Am = csr_matrix(array([[-2,1,0,0,0,9],
[1,-2,1,0,5,0],
[0,1,-2,1,0,0],
[0,0,1,-2,1,0],
[0,3,0,1,-2,1],
[1,0,0,0,1,-2]]))
b = array([1,2,3,4,5,6])
count = [0]
def matvec(v):
count[0] += 1
return Am*v
A = LinearOperator(matvec=matvec, shape=Am.shape, dtype=Am.dtype)
def do_solve(**kw):
count[0] = 0
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag = gcrotmk(A, b, x0=zeros(A.shape[0]), tol=1e-14, **kw)
count_0 = count[0]
assert_(allclose(A*x0, b, rtol=1e-12, atol=1e-12), norm(A*x0-b))
return x0, count_0
class TestGCROTMK(object):
def test_preconditioner(self):
# Check that preconditioning works
pc = splu(Am.tocsc())
M = LinearOperator(matvec=pc.solve, shape=A.shape, dtype=A.dtype)
x0, count_0 = do_solve()
x1, count_1 = do_solve(M=M)
assert_equal(count_1, 3)
assert_(count_1 < count_0/2)
assert_(allclose(x1, x0, rtol=1e-14))
def test_arnoldi(self):
np.random.rand(1234)
A = eye(10000) + rand(10000,10000,density=1e-4)
b = np.random.rand(10000)
# The inner arnoldi should be equivalent to gmres
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag0 = gcrotmk(A, b, x0=zeros(A.shape[0]), m=15, k=0, maxiter=1)
x1, flag1 = gmres(A, b, x0=zeros(A.shape[0]), restart=15, maxiter=1)
assert_equal(flag0, 1)
assert_equal(flag1, 1)
assert_(np.linalg.norm(A.dot(x0) - b) > 1e-3)
assert_allclose(x0, x1)
def test_cornercase(self):
np.random.seed(1234)
# Rounding error may prevent convergence with tol=0 --- ensure
# that the return values in this case are correct, and no
# exceptions are raised
for n in [3, 5, 10, 100]:
A = 2*eye(n)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
b = np.ones(n)
x, info = gcrotmk(A, b, maxiter=10)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
x, info = gcrotmk(A, b, tol=0, maxiter=10)
if info == 0:
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
b = np.random.rand(n)
x, info = gcrotmk(A, b, maxiter=10)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
x, info = gcrotmk(A, b, tol=0, maxiter=10)
if info == 0:
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
def test_nans(self):
A = eye(3, format='lil')
A[1,1] = np.nan
b = np.ones(3)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, info = gcrotmk(A, b, tol=0, maxiter=10)
assert_equal(info, 1)
def test_truncate(self):
np.random.seed(1234)
A = np.random.rand(30, 30) + np.eye(30)
b = np.random.rand(30)
for truncate in ['oldest', 'smallest']:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, info = gcrotmk(A, b, m=10, k=10, truncate=truncate, tol=1e-4,
maxiter=200)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-3)
def test_CU(self):
for discard_C in (True, False):
# Check that C,U behave as expected
CU = []
x0, count_0 = do_solve(CU=CU, discard_C=discard_C)
assert_(len(CU) > 0)
assert_(len(CU) <= 6)
if discard_C:
for c, u in CU:
assert_(c is None)
# should converge immediately
x1, count_1 = do_solve(CU=CU, discard_C=discard_C)
if discard_C:
assert_equal(count_1, 2 + len(CU))
else:
assert_equal(count_1, 3)
assert_(count_1 <= count_0/2)
assert_allclose(x1, x0, atol=1e-14)
def test_denormals(self):
# Check that no warnings are emitted if the matrix contains
# numbers for which 1/x has no float representation, and that
# the solver behaves properly.
A = np.array([[1, 2], [3, 4]], dtype=float)
A *= 100 * np.nextafter(0, 1)
b = np.array([1, 1])
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
xp, info = gcrotmk(A, b)
if info == 0:
assert_allclose(A.dot(xp), b)
| 5,493 | 31.702381 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/test_lsmr.py
|
"""
Copyright (C) 2010 David Fong and Michael Saunders
Distributed under the same license as Scipy
Testing Code for LSMR.
03 Jun 2010: First version release with lsmr.py
David Chin-lung Fong clfong@stanford.edu
Institute for Computational and Mathematical Engineering
Stanford University
Michael Saunders saunders@stanford.edu
Systems Optimization Laboratory
Dept of MS&E, Stanford University.
"""
from __future__ import division, print_function, absolute_import
from numpy import array, arange, eye, zeros, ones, sqrt, transpose, hstack
from numpy.linalg import norm
from numpy.testing import (assert_almost_equal,
assert_array_almost_equal)
from scipy.sparse import coo_matrix
from scipy.sparse.linalg.interface import aslinearoperator
from scipy.sparse.linalg import lsmr
from .test_lsqr import G, b
class TestLSMR:
def setup_method(self):
self.n = 10
self.m = 10
def assertCompatibleSystem(self, A, xtrue):
Afun = aslinearoperator(A)
b = Afun.matvec(xtrue)
x = lsmr(A, b)[0]
assert_almost_equal(norm(x - xtrue), 0, decimal=5)
def testIdentityACase1(self):
A = eye(self.n)
xtrue = zeros((self.n, 1))
self.assertCompatibleSystem(A, xtrue)
def testIdentityACase2(self):
A = eye(self.n)
xtrue = ones((self.n,1))
self.assertCompatibleSystem(A, xtrue)
def testIdentityACase3(self):
A = eye(self.n)
xtrue = transpose(arange(self.n,0,-1))
self.assertCompatibleSystem(A, xtrue)
def testBidiagonalA(self):
A = lowerBidiagonalMatrix(20,self.n)
xtrue = transpose(arange(self.n,0,-1))
self.assertCompatibleSystem(A,xtrue)
def testScalarB(self):
A = array([[1.0, 2.0]])
b = 3.0
x = lsmr(A, b)[0]
assert_almost_equal(norm(A.dot(x) - b), 0)
def testColumnB(self):
A = eye(self.n)
b = ones((self.n, 1))
x = lsmr(A, b)[0]
assert_almost_equal(norm(A.dot(x) - b.ravel()), 0)
def testInitialization(self):
# Test that the default setting is not modified
x_ref = lsmr(G, b)[0]
x0 = zeros(b.shape)
x = lsmr(G, b, x0=x0)[0]
assert_array_almost_equal(x_ref, x)
# Test warm-start with single iteration
x0 = lsmr(G, b, maxiter=1)[0]
x = lsmr(G, b, x0=x0)[0]
assert_array_almost_equal(x_ref, x)
class TestLSMRReturns:
def setup_method(self):
self.n = 10
self.A = lowerBidiagonalMatrix(20,self.n)
self.xtrue = transpose(arange(self.n,0,-1))
self.Afun = aslinearoperator(self.A)
self.b = self.Afun.matvec(self.xtrue)
self.returnValues = lsmr(self.A,self.b)
def testNormr(self):
x, istop, itn, normr, normar, normA, condA, normx = self.returnValues
assert_almost_equal(normr, norm(self.b - self.Afun.matvec(x)))
def testNormar(self):
x, istop, itn, normr, normar, normA, condA, normx = self.returnValues
assert_almost_equal(normar,
norm(self.Afun.rmatvec(self.b - self.Afun.matvec(x))))
def testNormx(self):
x, istop, itn, normr, normar, normA, condA, normx = self.returnValues
assert_almost_equal(normx, norm(x))
def lowerBidiagonalMatrix(m, n):
# This is a simple example for testing LSMR.
# It uses the leading m*n submatrix from
# A = [ 1
# 1 2
# 2 3
# 3 4
# ...
# n ]
# suitably padded by zeros.
#
# 04 Jun 2010: First version for distribution with lsmr.py
if m <= n:
row = hstack((arange(m, dtype=int),
arange(1, m, dtype=int)))
col = hstack((arange(m, dtype=int),
arange(m-1, dtype=int)))
data = hstack((arange(1, m+1, dtype=float),
arange(1,m, dtype=float)))
return coo_matrix((data, (row, col)), shape=(m,n))
else:
row = hstack((arange(n, dtype=int),
arange(1, n+1, dtype=int)))
col = hstack((arange(n, dtype=int),
arange(n, dtype=int)))
data = hstack((arange(1, n+1, dtype=float),
arange(1,n+1, dtype=float)))
return coo_matrix((data,(row, col)), shape=(m,n))
def lsmrtest(m, n, damp):
"""Verbose testing of lsmr"""
A = lowerBidiagonalMatrix(m,n)
xtrue = arange(n,0,-1, dtype=float)
Afun = aslinearoperator(A)
b = Afun.matvec(xtrue)
atol = 1.0e-7
btol = 1.0e-7
conlim = 1.0e+10
itnlim = 10*n
show = 1
x, istop, itn, normr, normar, norma, conda, normx \
= lsmr(A, b, damp, atol, btol, conlim, itnlim, show)
j1 = min(n,5)
j2 = max(n-4,1)
print(' ')
print('First elements of x:')
str = ['%10.4f' % (xi) for xi in x[0:j1]]
print(''.join(str))
print(' ')
print('Last elements of x:')
str = ['%10.4f' % (xi) for xi in x[j2-1:]]
print(''.join(str))
r = b - Afun.matvec(x)
r2 = sqrt(norm(r)**2 + (damp*norm(x))**2)
print(' ')
str = 'normr (est.) %17.10e' % (normr)
str2 = 'normr (true) %17.10e' % (r2)
print(str)
print(str2)
print(' ')
if __name__ == "__main__":
lsmrtest(20,10,0)
| 5,317 | 28.381215 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/test_lgmres.py
|
"""Tests for the linalg.isolve.lgmres module
"""
from __future__ import division, print_function, absolute_import
from numpy.testing import assert_, assert_allclose, assert_equal
import numpy as np
from numpy import zeros, array, allclose
from scipy.linalg import norm
from scipy.sparse import csr_matrix, eye, rand
from scipy.sparse.linalg.interface import LinearOperator
from scipy.sparse.linalg import splu
from scipy.sparse.linalg.isolve import lgmres, gmres
from scipy._lib._numpy_compat import suppress_warnings
Am = csr_matrix(array([[-2,1,0,0,0,9],
[1,-2,1,0,5,0],
[0,1,-2,1,0,0],
[0,0,1,-2,1,0],
[0,3,0,1,-2,1],
[1,0,0,0,1,-2]]))
b = array([1,2,3,4,5,6])
count = [0]
def matvec(v):
count[0] += 1
return Am*v
A = LinearOperator(matvec=matvec, shape=Am.shape, dtype=Am.dtype)
def do_solve(**kw):
count[0] = 0
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag = lgmres(A, b, x0=zeros(A.shape[0]), inner_m=6, tol=1e-14, **kw)
count_0 = count[0]
assert_(allclose(A*x0, b, rtol=1e-12, atol=1e-12), norm(A*x0-b))
return x0, count_0
class TestLGMRES(object):
def test_preconditioner(self):
# Check that preconditioning works
pc = splu(Am.tocsc())
M = LinearOperator(matvec=pc.solve, shape=A.shape, dtype=A.dtype)
x0, count_0 = do_solve()
x1, count_1 = do_solve(M=M)
assert_(count_1 == 3)
assert_(count_1 < count_0/2)
assert_(allclose(x1, x0, rtol=1e-14))
def test_outer_v(self):
# Check that the augmentation vectors behave as expected
outer_v = []
x0, count_0 = do_solve(outer_k=6, outer_v=outer_v)
assert_(len(outer_v) > 0)
assert_(len(outer_v) <= 6)
x1, count_1 = do_solve(outer_k=6, outer_v=outer_v, prepend_outer_v=True)
assert_(count_1 == 2, count_1)
assert_(count_1 < count_0/2)
assert_(allclose(x1, x0, rtol=1e-14))
# ---
outer_v = []
x0, count_0 = do_solve(outer_k=6, outer_v=outer_v, store_outer_Av=False)
assert_(array([v[1] is None for v in outer_v]).all())
assert_(len(outer_v) > 0)
assert_(len(outer_v) <= 6)
x1, count_1 = do_solve(outer_k=6, outer_v=outer_v, prepend_outer_v=True)
assert_(count_1 == 3, count_1)
assert_(count_1 < count_0/2)
assert_(allclose(x1, x0, rtol=1e-14))
def test_arnoldi(self):
np.random.rand(1234)
A = eye(10000) + rand(10000,10000,density=1e-4)
b = np.random.rand(10000)
# The inner arnoldi should be equivalent to gmres
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag0 = lgmres(A, b, x0=zeros(A.shape[0]), inner_m=15, maxiter=1)
x1, flag1 = gmres(A, b, x0=zeros(A.shape[0]), restart=15, maxiter=1)
assert_equal(flag0, 1)
assert_equal(flag1, 1)
assert_(np.linalg.norm(A.dot(x0) - b) > 1e-3)
assert_allclose(x0, x1)
def test_cornercase(self):
np.random.seed(1234)
# Rounding error may prevent convergence with tol=0 --- ensure
# that the return values in this case are correct, and no
# exceptions are raised
for n in [3, 5, 10, 100]:
A = 2*eye(n)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
b = np.ones(n)
x, info = lgmres(A, b, maxiter=10)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
x, info = lgmres(A, b, tol=0, maxiter=10)
if info == 0:
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
b = np.random.rand(n)
x, info = lgmres(A, b, maxiter=10)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
x, info = lgmres(A, b, tol=0, maxiter=10)
if info == 0:
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
def test_nans(self):
A = eye(3, format='lil')
A[1,1] = np.nan
b = np.ones(3)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, info = lgmres(A, b, tol=0, maxiter=10)
assert_equal(info, 1)
def test_breakdown_with_outer_v(self):
A = np.array([[1, 2], [3, 4]], dtype=float)
b = np.array([1, 2])
x = np.linalg.solve(A, b)
v0 = np.array([1, 0])
# The inner iteration should converge to the correct solution,
# since it's in the outer vector list
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
xp, info = lgmres(A, b, outer_v=[(v0, None), (x, None)], maxiter=1)
assert_allclose(xp, x, atol=1e-12)
def test_breakdown_underdetermined(self):
# Should find LSQ solution in the Krylov span in one inner
# iteration, despite solver breakdown from nilpotent A.
A = np.array([[0, 1, 1, 1],
[0, 0, 1, 1],
[0, 0, 0, 1],
[0, 0, 0, 0]], dtype=float)
bs = [
np.array([1, 1, 1, 1]),
np.array([1, 1, 1, 0]),
np.array([1, 1, 0, 0]),
np.array([1, 0, 0, 0]),
]
for b in bs:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
xp, info = lgmres(A, b, maxiter=1)
resp = np.linalg.norm(A.dot(xp) - b)
K = np.c_[b, A.dot(b), A.dot(A.dot(b)), A.dot(A.dot(A.dot(b)))]
y, _, _, _ = np.linalg.lstsq(A.dot(K), b, rcond=-1)
x = K.dot(y)
res = np.linalg.norm(A.dot(x) - b)
assert_allclose(resp, res, err_msg=repr(b))
def test_denormals(self):
# Check that no warnings are emitted if the matrix contains
# numbers for which 1/x has no float representation, and that
# the solver behaves properly.
A = np.array([[1, 2], [3, 4]], dtype=float)
A *= 100 * np.nextafter(0, 1)
b = np.array([1, 1])
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
xp, info = lgmres(A, b)
if info == 0:
assert_allclose(A.dot(xp), b)
| 6,722 | 31.955882 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/demo_lgmres.py
|
from __future__ import division, print_function, absolute_import
import scipy.sparse.linalg as la
import scipy.sparse as sp
import scipy.io as io
import numpy as np
import sys
#problem = "SPARSKIT/drivcav/e05r0100"
problem = "SPARSKIT/drivcav/e05r0200"
#problem = "Harwell-Boeing/sherman/sherman1"
#problem = "misc/hamm/add32"
mm = np.lib._datasource.Repository('ftp://math.nist.gov/pub/MatrixMarket2/')
f = mm.open('%s.mtx.gz' % problem)
Am = io.mmread(f).tocsr()
f.close()
f = mm.open('%s_rhs1.mtx.gz' % problem)
b = np.array(io.mmread(f)).ravel()
f.close()
count = [0]
def matvec(v):
count[0] += 1
sys.stderr.write('%d\r' % count[0])
return Am*v
A = la.LinearOperator(matvec=matvec, shape=Am.shape, dtype=Am.dtype)
M = 100
print("MatrixMarket problem %s" % problem)
print("Invert %d x %d matrix; nnz = %d" % (Am.shape[0], Am.shape[1], Am.nnz))
count[0] = 0
x0, info = la.gmres(A, b, restrt=M, tol=1e-14)
count_0 = count[0]
err0 = np.linalg.norm(Am*x0 - b) / np.linalg.norm(b)
print("GMRES(%d):" % M, count_0, "matvecs, residual", err0)
if info != 0:
print("Didn't converge")
count[0] = 0
x1, info = la.lgmres(A, b, inner_m=M-6*2, outer_k=6, tol=1e-14)
count_1 = count[0]
err1 = np.linalg.norm(Am*x1 - b) / np.linalg.norm(b)
print("LGMRES(%d,6) [same memory req.]:" % (M-2*6), count_1,
"matvecs, residual:", err1)
if info != 0:
print("Didn't converge")
count[0] = 0
x2, info = la.lgmres(A, b, inner_m=M-6, outer_k=6, tol=1e-14)
count_2 = count[0]
err2 = np.linalg.norm(Am*x2 - b) / np.linalg.norm(b)
print("LGMRES(%d,6) [same subspace size]:" % (M-6), count_2,
"matvecs, residual:", err2)
if info != 0:
print("Didn't converge")
| 1,680 | 25.265625 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/test_lsqr.py
|
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import (assert_, assert_equal, assert_almost_equal,
assert_array_almost_equal)
from scipy._lib.six import xrange
import scipy.sparse
import scipy.sparse.linalg
from scipy.sparse.linalg import lsqr
from time import time
# Set up a test problem
n = 35
G = np.eye(n)
normal = np.random.normal
norm = np.linalg.norm
for jj in xrange(5):
gg = normal(size=n)
hh = gg * gg.T
G += (hh + hh.T) * 0.5
G += normal(size=n) * normal(size=n)
b = normal(size=n)
tol = 1e-10
show = False
maxit = None
def test_basic():
b_copy = b.copy()
X = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit)
assert_(np.all(b_copy == b))
svx = np.linalg.solve(G, b)
xo = X[0]
assert_(norm(svx - xo) < 1e-5)
def test_gh_2466():
row = np.array([0, 0])
col = np.array([0, 1])
val = np.array([1, -1])
A = scipy.sparse.coo_matrix((val, (row, col)), shape=(1, 2))
b = np.asarray([4])
lsqr(A, b)
def test_well_conditioned_problems():
# Test that sparse the lsqr solver returns the right solution
# on various problems with different random seeds.
# This is a non-regression test for a potential ZeroDivisionError
# raised when computing the `test2` & `test3` convergence conditions.
n = 10
A_sparse = scipy.sparse.eye(n, n)
A_dense = A_sparse.toarray()
with np.errstate(invalid='raise'):
for seed in range(30):
rng = np.random.RandomState(seed + 10)
beta = rng.rand(n)
beta[beta == 0] = 0.00001 # ensure that all the betas are not null
b = A_sparse * beta[:, np.newaxis]
output = lsqr(A_sparse, b, show=show)
# Check that the termination condition corresponds to an approximate
# solution to Ax = b
assert_equal(output[1], 1)
solution = output[0]
# Check that we recover the ground truth solution
assert_array_almost_equal(solution, beta)
# Sanity check: compare to the dense array solver
reference_solution = np.linalg.solve(A_dense, b).ravel()
assert_array_almost_equal(solution, reference_solution)
def test_b_shapes():
# Test b being a scalar.
A = np.array([[1.0, 2.0]])
b = 3.0
x = lsqr(A, b)[0]
assert_almost_equal(norm(A.dot(x) - b), 0)
# Test b being a column vector.
A = np.eye(10)
b = np.ones((10, 1))
x = lsqr(A, b)[0]
assert_almost_equal(norm(A.dot(x) - b.ravel()), 0)
def test_initialization():
# Test the default setting is the same as zeros
b_copy = b.copy()
x_ref = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit)
x0 = np.zeros(x_ref[0].shape)
x = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit, x0=x0)
assert_(np.all(b_copy == b))
assert_array_almost_equal(x_ref[0], x[0])
# Test warm-start with single iteration
x0 = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=1)[0]
x = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit, x0=x0)
assert_array_almost_equal(x_ref[0], x[0])
assert_(np.all(b_copy == b))
if __name__ == "__main__":
svx = np.linalg.solve(G, b)
tic = time()
X = lsqr(G, b, show=show, atol=tol, btol=tol, iter_lim=maxit)
xo = X[0]
phio = X[3]
psio = X[7]
k = X[2]
chio = X[8]
mg = np.amax(G - G.T)
if mg > 1e-14:
sym = 'No'
else:
sym = 'Yes'
print('LSQR')
print("Is linear operator symmetric? " + sym)
print("n: %3g iterations: %3g" % (n, k))
print("Norms computed in %.2fs by LSQR" % (time() - tic))
print(" ||x|| %9.4e ||r|| %9.4e ||Ar|| %9.4e " % (chio, phio, psio))
print("Residual norms computed directly:")
print(" ||x|| %9.4e ||r|| %9.4e ||Ar|| %9.4e" % (norm(xo),
norm(G*xo - b),
norm(G.T*(G*xo-b))))
print("Direct solution norms:")
print(" ||x|| %9.4e ||r|| %9.4e " % (norm(svx), norm(G*svx - b)))
print("")
print(" || x_{direct} - x_{LSQR}|| %9.4e " % norm(svx-xo))
print("")
| 4,268 | 29.492857 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/test_iterative.py
|
""" Test functions for the sparse.linalg.isolve module
"""
from __future__ import division, print_function, absolute_import
import itertools
import numpy as np
from numpy.testing import (assert_equal, assert_array_equal,
assert_, assert_allclose)
import pytest
from pytest import raises as assert_raises
from scipy._lib._numpy_compat import suppress_warnings
from numpy import zeros, arange, array, ones, eye, iscomplexobj
from scipy.linalg import norm
from scipy.sparse import spdiags, csr_matrix, SparseEfficiencyWarning
from scipy.sparse.linalg import LinearOperator, aslinearoperator
from scipy.sparse.linalg.isolve import cg, cgs, bicg, bicgstab, gmres, qmr, minres, lgmres, gcrotmk
# TODO check that method preserve shape and type
# TODO test both preconditioner methods
class Case(object):
def __init__(self, name, A, skip=None):
self.name = name
self.A = A
if skip is None:
self.skip = []
else:
self.skip = skip
def __repr__(self):
return "<%s>" % self.name
class IterativeParams(object):
def __init__(self):
# list of tuples (solver, symmetric, positive_definite )
solvers = [cg, cgs, bicg, bicgstab, gmres, qmr, minres, lgmres, gcrotmk]
sym_solvers = [minres, cg]
posdef_solvers = [cg]
real_solvers = [minres]
self.solvers = solvers
# list of tuples (A, symmetric, positive_definite )
self.cases = []
# Symmetric and Positive Definite
N = 40
data = ones((3,N))
data[0,:] = 2
data[1,:] = -1
data[2,:] = -1
Poisson1D = spdiags(data, [0,-1,1], N, N, format='csr')
self.Poisson1D = Case("poisson1d", Poisson1D)
self.cases.append(Case("poisson1d", Poisson1D))
# note: minres fails for single precision
self.cases.append(Case("poisson1d", Poisson1D.astype('f'),
skip=[minres]))
# Symmetric and Negative Definite
self.cases.append(Case("neg-poisson1d", -Poisson1D,
skip=posdef_solvers))
# note: minres fails for single precision
self.cases.append(Case("neg-poisson1d", (-Poisson1D).astype('f'),
skip=posdef_solvers + [minres]))
# Symmetric and Indefinite
data = array([[6, -5, 2, 7, -1, 10, 4, -3, -8, 9]],dtype='d')
RandDiag = spdiags(data, [0], 10, 10, format='csr')
self.cases.append(Case("rand-diag", RandDiag, skip=posdef_solvers))
self.cases.append(Case("rand-diag", RandDiag.astype('f'),
skip=posdef_solvers))
# Random real-valued
np.random.seed(1234)
data = np.random.rand(4, 4)
self.cases.append(Case("rand", data, skip=posdef_solvers+sym_solvers))
self.cases.append(Case("rand", data.astype('f'),
skip=posdef_solvers+sym_solvers))
# Random symmetric real-valued
np.random.seed(1234)
data = np.random.rand(4, 4)
data = data + data.T
self.cases.append(Case("rand-sym", data, skip=posdef_solvers))
self.cases.append(Case("rand-sym", data.astype('f'),
skip=posdef_solvers))
# Random pos-def symmetric real
np.random.seed(1234)
data = np.random.rand(9, 9)
data = np.dot(data.conj(), data.T)
self.cases.append(Case("rand-sym-pd", data))
# note: minres fails for single precision
self.cases.append(Case("rand-sym-pd", data.astype('f'),
skip=[minres]))
# Random complex-valued
np.random.seed(1234)
data = np.random.rand(4, 4) + 1j*np.random.rand(4, 4)
self.cases.append(Case("rand-cmplx", data,
skip=posdef_solvers+sym_solvers+real_solvers))
self.cases.append(Case("rand-cmplx", data.astype('F'),
skip=posdef_solvers+sym_solvers+real_solvers))
# Random hermitian complex-valued
np.random.seed(1234)
data = np.random.rand(4, 4) + 1j*np.random.rand(4, 4)
data = data + data.T.conj()
self.cases.append(Case("rand-cmplx-herm", data,
skip=posdef_solvers+real_solvers))
self.cases.append(Case("rand-cmplx-herm", data.astype('F'),
skip=posdef_solvers+real_solvers))
# Random pos-def hermitian complex-valued
np.random.seed(1234)
data = np.random.rand(9, 9) + 1j*np.random.rand(9, 9)
data = np.dot(data.conj(), data.T)
self.cases.append(Case("rand-cmplx-sym-pd", data, skip=real_solvers))
self.cases.append(Case("rand-cmplx-sym-pd", data.astype('F'),
skip=real_solvers))
# Non-symmetric and Positive Definite
#
# cgs, qmr, and bicg fail to converge on this one
# -- algorithmic limitation apparently
data = ones((2,10))
data[0,:] = 2
data[1,:] = -1
A = spdiags(data, [0,-1], 10, 10, format='csr')
self.cases.append(Case("nonsymposdef", A,
skip=sym_solvers+[cgs, qmr, bicg]))
self.cases.append(Case("nonsymposdef", A.astype('F'),
skip=sym_solvers+[cgs, qmr, bicg]))
params = IterativeParams()
def check_maxiter(solver, case):
A = case.A
tol = 1e-12
b = arange(A.shape[0], dtype=float)
x0 = 0*b
residuals = []
def callback(x):
residuals.append(norm(b - case.A*x))
x, info = solver(A, b, x0=x0, tol=tol, maxiter=1, callback=callback)
assert_equal(len(residuals), 1)
assert_equal(info, 1)
def test_maxiter():
case = params.Poisson1D
for solver in params.solvers:
if solver in case.skip:
continue
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
check_maxiter(solver, case)
def assert_normclose(a, b, tol=1e-8):
residual = norm(a - b)
tolerance = tol*norm(b)
msg = "residual (%g) not smaller than tolerance %g" % (residual, tolerance)
assert_(residual < tolerance, msg=msg)
def check_convergence(solver, case):
A = case.A
if A.dtype.char in "dD":
tol = 1e-8
else:
tol = 1e-2
b = arange(A.shape[0], dtype=A.dtype)
x0 = 0*b
x, info = solver(A, b, x0=x0, tol=tol)
assert_array_equal(x0, 0*b) # ensure that x0 is not overwritten
assert_equal(info,0)
assert_normclose(A.dot(x), b, tol=tol)
def test_convergence():
for solver in params.solvers:
for case in params.cases:
if solver in case.skip:
continue
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
check_convergence(solver, case)
def check_precond_dummy(solver, case):
tol = 1e-8
def identity(b,which=None):
"""trivial preconditioner"""
return b
A = case.A
M,N = A.shape
D = spdiags([1.0/A.diagonal()], [0], M, N)
b = arange(A.shape[0], dtype=float)
x0 = 0*b
precond = LinearOperator(A.shape, identity, rmatvec=identity)
if solver is qmr:
x, info = solver(A, b, M1=precond, M2=precond, x0=x0, tol=tol)
else:
x, info = solver(A, b, M=precond, x0=x0, tol=tol)
assert_equal(info,0)
assert_normclose(A.dot(x), b, tol)
A = aslinearoperator(A)
A.psolve = identity
A.rpsolve = identity
x, info = solver(A, b, x0=x0, tol=tol)
assert_equal(info,0)
assert_normclose(A*x, b, tol=tol)
def test_precond_dummy():
case = params.Poisson1D
for solver in params.solvers:
if solver in case.skip:
continue
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
check_precond_dummy(solver, case)
def check_precond_inverse(solver, case):
tol = 1e-8
def inverse(b,which=None):
"""inverse preconditioner"""
A = case.A
if not isinstance(A, np.ndarray):
A = A.todense()
return np.linalg.solve(A, b)
def rinverse(b,which=None):
"""inverse preconditioner"""
A = case.A
if not isinstance(A, np.ndarray):
A = A.todense()
return np.linalg.solve(A.T, b)
matvec_count = [0]
def matvec(b):
matvec_count[0] += 1
return case.A.dot(b)
def rmatvec(b):
matvec_count[0] += 1
return case.A.T.dot(b)
b = arange(case.A.shape[0], dtype=float)
x0 = 0*b
A = LinearOperator(case.A.shape, matvec, rmatvec=rmatvec)
precond = LinearOperator(case.A.shape, inverse, rmatvec=rinverse)
# Solve with preconditioner
matvec_count = [0]
x, info = solver(A, b, M=precond, x0=x0, tol=tol)
assert_equal(info, 0)
assert_normclose(case.A.dot(x), b, tol)
# Solution should be nearly instant
assert_(matvec_count[0] <= 3, repr(matvec_count))
def test_precond_inverse():
case = params.Poisson1D
for solver in params.solvers:
if solver in case.skip:
continue
if solver is qmr:
continue
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
check_precond_inverse(solver, case)
def test_gmres_basic():
A = np.vander(np.arange(10) + 1)[:, ::-1]
b = np.zeros(10)
b[0] = 1
x = np.linalg.solve(A, b)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x_gm, err = gmres(A, b, restart=5, maxiter=1)
assert_allclose(x_gm[0], 0.359, rtol=1e-2)
def test_reentrancy():
non_reentrant = [cg, cgs, bicg, bicgstab, gmres, qmr]
reentrant = [lgmres, minres, gcrotmk]
for solver in reentrant + non_reentrant:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
_check_reentrancy(solver, solver in reentrant)
def _check_reentrancy(solver, is_reentrant):
def matvec(x):
A = np.array([[1.0, 0, 0], [0, 2.0, 0], [0, 0, 3.0]])
y, info = solver(A, x)
assert_equal(info, 0)
return y
b = np.array([1, 1./2, 1./3])
op = LinearOperator((3, 3), matvec=matvec, rmatvec=matvec,
dtype=b.dtype)
if not is_reentrant:
assert_raises(RuntimeError, solver, op, b)
else:
y, info = solver(op, b)
assert_equal(info, 0)
assert_allclose(y, [1, 1, 1])
@pytest.mark.parametrize("solver", [cg, cgs, bicg, bicgstab, gmres, qmr, lgmres, gcrotmk])
def test_atol(solver):
# TODO: minres. It didn't historically use absolute tolerances, so
# fixing it is less urgent.
np.random.seed(1234)
A = np.random.rand(10, 10)
A = A.dot(A.T) + 10 * np.eye(10)
b = 1e3 * np.random.rand(10)
b_norm = np.linalg.norm(b)
tols = np.r_[0, np.logspace(np.log10(1e-10), np.log10(1e2), 7), np.inf]
# Check effect of badly scaled preconditioners
M0 = np.random.randn(10, 10)
M0 = M0.dot(M0.T)
Ms = [None, 1e-6 * M0, 1e6 * M0]
for M, tol, atol in itertools.product(Ms, tols, tols):
if tol == 0 and atol == 0:
continue
if solver is qmr:
if M is not None:
M = aslinearoperator(M)
M2 = aslinearoperator(np.eye(10))
else:
M2 = None
x, info = solver(A, b, M1=M, M2=M2, tol=tol, atol=atol)
else:
x, info = solver(A, b, M=M, tol=tol, atol=atol)
assert_equal(info, 0)
residual = A.dot(x) - b
err = np.linalg.norm(residual)
atol2 = tol * b_norm
assert_(err <= max(atol, atol2))
@pytest.mark.parametrize("solver", [cg, cgs, bicg, bicgstab, gmres, qmr, minres, lgmres, gcrotmk])
def test_zero_rhs(solver):
np.random.seed(1234)
A = np.random.rand(10, 10)
A = A.dot(A.T) + 10 * np.eye(10)
b = np.zeros(10)
tols = np.r_[np.logspace(np.log10(1e-10), np.log10(1e2), 7)]
for tol in tols:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, info = solver(A, b, tol=tol)
assert_equal(info, 0)
assert_allclose(x, 0, atol=1e-15)
x, info = solver(A, b, tol=tol, x0=ones(10))
assert_equal(info, 0)
assert_allclose(x, 0, atol=tol)
if solver is not minres:
x, info = solver(A, b, tol=tol, atol=0, x0=ones(10))
if info == 0:
assert_allclose(x, 0)
x, info = solver(A, b, tol=tol, atol=tol)
assert_equal(info, 0)
assert_allclose(x, 0, atol=1e-300)
x, info = solver(A, b, tol=tol, atol=0)
assert_equal(info, 0)
assert_allclose(x, 0, atol=1e-300)
#------------------------------------------------------------------------------
class TestQMR(object):
def test_leftright_precond(self):
"""Check that QMR works with left and right preconditioners"""
from scipy.sparse.linalg.dsolve import splu
from scipy.sparse.linalg.interface import LinearOperator
n = 100
dat = ones(n)
A = spdiags([-2*dat, 4*dat, -dat], [-1,0,1],n,n)
b = arange(n,dtype='d')
L = spdiags([-dat/2, dat], [-1,0], n, n)
U = spdiags([4*dat, -dat], [0,1], n, n)
with suppress_warnings() as sup:
sup.filter(SparseEfficiencyWarning, "splu requires CSC matrix format")
L_solver = splu(L)
U_solver = splu(U)
def L_solve(b):
return L_solver.solve(b)
def U_solve(b):
return U_solver.solve(b)
def LT_solve(b):
return L_solver.solve(b,'T')
def UT_solve(b):
return U_solver.solve(b,'T')
M1 = LinearOperator((n,n), matvec=L_solve, rmatvec=LT_solve)
M2 = LinearOperator((n,n), matvec=U_solve, rmatvec=UT_solve)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x,info = qmr(A, b, tol=1e-8, maxiter=15, M1=M1, M2=M2)
assert_equal(info,0)
assert_normclose(A*x, b, tol=1e-8)
class TestGMRES(object):
def test_callback(self):
def store_residual(r, rvec):
rvec[rvec.nonzero()[0].max()+1] = r
# Define, A,b
A = csr_matrix(array([[-2,1,0,0,0,0],[1,-2,1,0,0,0],[0,1,-2,1,0,0],[0,0,1,-2,1,0],[0,0,0,1,-2,1],[0,0,0,0,1,-2]]))
b = ones((A.shape[0],))
maxiter = 1
rvec = zeros(maxiter+1)
rvec[0] = 1.0
callback = lambda r:store_residual(r, rvec)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x,flag = gmres(A, b, x0=zeros(A.shape[0]), tol=1e-16, maxiter=maxiter, callback=callback)
# Expected output from Scipy 1.0.0
assert_allclose(rvec, array([1.0, 0.81649658092772603]), rtol=1e-10)
# Test preconditioned callback
M = 1e-3 * np.eye(A.shape[0])
rvec = zeros(maxiter+1)
rvec[0] = 1.0
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, flag = gmres(A, b, M=M, tol=1e-16, maxiter=maxiter, callback=callback)
# Expected output from Scipy 1.0.0 (callback has preconditioned residual!)
assert_allclose(rvec, array([1.0, 1e-3 * 0.81649658092772603]), rtol=1e-10)
def test_abi(self):
# Check we don't segfault on gmres with complex argument
A = eye(2)
b = ones(2)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
r_x, r_info = gmres(A, b)
r_x = r_x.astype(complex)
x, info = gmres(A.astype(complex), b.astype(complex))
assert_(iscomplexobj(x))
assert_allclose(r_x, x)
assert_(r_info == info)
def test_atol_legacy(self):
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
# Check the strange legacy behavior: the tolerance is interpreted
# as atol, but only for the initial residual
A = eye(2)
b = 1e-6 * ones(2)
x, info = gmres(A, b, tol=1e-5)
assert_array_equal(x, np.zeros(2))
A = eye(2)
b = ones(2)
x, info = gmres(A, b, tol=1e-5)
assert_(np.linalg.norm(A.dot(x) - b) <= 1e-5*np.linalg.norm(b))
assert_allclose(x, b, atol=0, rtol=1e-8)
A = np.random.rand(30, 30)
b = 1e-6 * ones(30)
x, info = gmres(A, b, tol=1e-7, restart=20)
assert_(np.linalg.norm(A.dot(x) - b) > 1e-7)
A = eye(2)
b = 1e-10 * ones(2)
x, info = gmres(A, b, tol=1e-8, atol=0)
assert_(np.linalg.norm(A.dot(x) - b) <= 1e-8*np.linalg.norm(b))
def test_defective_precond_breakdown(self):
# Breakdown due to defective preconditioner
M = np.eye(3)
M[2,2] = 0
b = np.array([0, 1, 1])
x = np.array([1, 0, 0])
A = np.diag([2, 3, 4])
x, info = gmres(A, b, x0=x, M=M, tol=1e-15, atol=0)
# Should not return nans, nor terminate with false success
assert_(not np.isnan(x).any())
if info == 0:
assert_(np.linalg.norm(A.dot(x) - b) <= 1e-15*np.linalg.norm(b))
# The solution should be OK outside null space of M
assert_allclose(M.dot(A.dot(x)), M.dot(b))
def test_defective_matrix_breakdown(self):
# Breakdown due to defective matrix
A = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]])
b = np.array([1, 0, 1])
x, info = gmres(A, b, tol=1e-8, atol=0)
# Should not return nans, nor terminate with false success
assert_(not np.isnan(x).any())
if info == 0:
assert_(np.linalg.norm(A.dot(x) - b) <= 1e-8*np.linalg.norm(b))
# The solution should be OK outside null space of A
assert_allclose(A.dot(A.dot(x)), A.dot(b))
| 18,459 | 31.272727 | 122 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/test_minres.py
|
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import assert_equal, assert_allclose, assert_
from scipy.sparse.linalg.isolve import minres
import pytest
from pytest import raises as assert_raises
from .test_iterative import assert_normclose
def get_sample_problem():
# A random 10 x 10 symmetric matrix
np.random.seed(1234)
matrix = np.random.rand(10, 10)
matrix = matrix + matrix.T
# A random vector of length 10
vector = np.random.rand(10)
return matrix, vector
def test_singular():
A, b = get_sample_problem()
A[0, ] = 0
b[0] = 0
xp, info = minres(A, b)
assert_equal(info, 0)
assert_normclose(A.dot(xp), b, tol=1e-5)
@pytest.mark.skip(reason="Skip Until gh #6843 is fixed")
def test_gh_6843():
"""check if x0 is being used by tracing iterates"""
A, b = get_sample_problem()
# Random x0 to feed minres
np.random.seed(12345)
x0 = np.random.rand(10)
trace = []
def trace_iterates(xk):
trace.append(xk)
minres(A, b, x0=x0, callback=trace_iterates)
trace_with_x0 = trace
trace = []
minres(A, b, callback=trace_iterates)
assert_(not np.array_equal(trace_with_x0[0], trace[0]))
def test_shift():
A, b = get_sample_problem()
shift = 0.5
shifted_A = A - shift * np.eye(10)
x1, info1 = minres(A, b, shift=shift)
x2, info2 = minres(shifted_A, b)
assert_equal(info1, 0)
assert_allclose(x1, x2, rtol=1e-5)
def test_asymmetric_fail():
"""Asymmetric matrix should raise `ValueError` when check=True"""
A, b = get_sample_problem()
A[1, 2] = 1
A[2, 1] = 2
with assert_raises(ValueError):
xp, info = minres(A, b, check=True)
| 1,743 | 25.424242 | 69 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/isolve/tests/test_utils.py
|
from __future__ import division, print_function, absolute_import
import numpy as np
from pytest import raises as assert_raises
from scipy.sparse.linalg import utils
def test_make_system_bad_shape():
assert_raises(ValueError, utils.make_system, np.zeros((5,3)), None, np.zeros(4), np.zeros(4))
| 301 | 26.454545 | 97 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/dsolve/setup.py
|
from __future__ import division, print_function, absolute_import
from os.path import join, dirname
import sys
import os
import glob
def configuration(parent_package='',top_path=None):
from numpy.distutils.misc_util import Configuration
from numpy.distutils.system_info import get_info
from scipy._build_utils import get_sgemv_fix
from scipy._build_utils import numpy_nodepr_api
config = Configuration('dsolve',parent_package,top_path)
config.add_data_dir('tests')
lapack_opt = get_info('lapack_opt',notfound_action=2)
if sys.platform == 'win32':
superlu_defs = [('NO_TIMER',1)]
else:
superlu_defs = []
superlu_defs.append(('USE_VENDOR_BLAS',1))
superlu_src = join(dirname(__file__), 'SuperLU', 'SRC')
sources = list(glob.glob(join(superlu_src, '*.c')))
headers = list(glob.glob(join(superlu_src, '*.h')))
config.add_library('superlu_src',
sources=sources,
macros=superlu_defs,
include_dirs=[superlu_src],
)
# Extension
ext_sources = ['_superlumodule.c',
'_superlu_utils.c',
'_superluobject.c']
ext_sources += get_sgemv_fix(lapack_opt)
config.add_extension('_superlu',
sources=ext_sources,
libraries=['superlu_src'],
depends=(sources + headers),
extra_info=lapack_opt,
**numpy_nodepr_api
)
# Add license files
config.add_data_files('SuperLU/License.txt')
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())
| 1,781 | 29.20339 | 64 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/dsolve/linsolve.py
|
from __future__ import division, print_function, absolute_import
from warnings import warn
import numpy as np
from numpy import asarray
from scipy.sparse import (isspmatrix_csc, isspmatrix_csr, isspmatrix,
SparseEfficiencyWarning, csc_matrix, csr_matrix)
from scipy.linalg import LinAlgError
from . import _superlu
noScikit = False
try:
import scikits.umfpack as umfpack
except ImportError:
noScikit = True
useUmfpack = not noScikit
__all__ = ['use_solver', 'spsolve', 'splu', 'spilu', 'factorized',
'MatrixRankWarning', 'spsolve_triangular']
class MatrixRankWarning(UserWarning):
pass
def use_solver(**kwargs):
"""
Select default sparse direct solver to be used.
Parameters
----------
useUmfpack : bool, optional
Use UMFPACK over SuperLU. Has effect only if scikits.umfpack is
installed. Default: True
assumeSortedIndices : bool, optional
Allow UMFPACK to skip the step of sorting indices for a CSR/CSC matrix.
Has effect only if useUmfpack is True and scikits.umfpack is installed.
Default: False
Notes
-----
The default sparse solver is umfpack when available
(scikits.umfpack is installed). This can be changed by passing
useUmfpack = False, which then causes the always present SuperLU
based solver to be used.
Umfpack requires a CSR/CSC matrix to have sorted column/row indices. If
sure that the matrix fulfills this, pass ``assumeSortedIndices=True``
to gain some speed.
"""
if 'useUmfpack' in kwargs:
globals()['useUmfpack'] = kwargs['useUmfpack']
if useUmfpack and 'assumeSortedIndices' in kwargs:
umfpack.configure(assumeSortedIndices=kwargs['assumeSortedIndices'])
def _get_umf_family(A):
"""Get umfpack family string given the sparse matrix dtype."""
_families = {
(np.float64, np.int32): 'di',
(np.complex128, np.int32): 'zi',
(np.float64, np.int64): 'dl',
(np.complex128, np.int64): 'zl'
}
f_type = np.sctypeDict[A.dtype.name]
i_type = np.sctypeDict[A.indices.dtype.name]
try:
family = _families[(f_type, i_type)]
except KeyError:
msg = 'only float64 or complex128 matrices with int32 or int64' \
' indices are supported! (got: matrix: %s, indices: %s)' \
% (f_type, i_type)
raise ValueError(msg)
return family
def spsolve(A, b, permc_spec=None, use_umfpack=True):
"""Solve the sparse linear system Ax=b, where b may be a vector or a matrix.
Parameters
----------
A : ndarray or sparse matrix
The square matrix A will be converted into CSC or CSR form
b : ndarray or sparse matrix
The matrix or vector representing the right hand side of the equation.
If a vector, b.shape must be (n,) or (n, 1).
permc_spec : str, optional
How to permute the columns of the matrix for sparsity preservation.
(default: 'COLAMD')
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering
use_umfpack : bool, optional
if True (default) then use umfpack for the solution. This is
only referenced if b is a vector and ``scikit-umfpack`` is installed.
Returns
-------
x : ndarray or sparse matrix
the solution of the sparse linear equation.
If b is a vector, then x is a vector of size A.shape[1]
If b is a matrix, then x is a matrix of size (A.shape[1], b.shape[1])
Notes
-----
For solving the matrix expression AX = B, this solver assumes the resulting
matrix X is sparse, as is often the case for very sparse inputs. If the
resulting X is dense, the construction of this sparse result will be
relatively expensive. In that case, consider converting A to a dense
matrix and using scipy.linalg.solve or its variants.
Examples
--------
>>> from scipy.sparse import csc_matrix
>>> from scipy.sparse.linalg import spsolve
>>> A = csc_matrix([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
>>> B = csc_matrix([[2, 0], [-1, 0], [2, 0]], dtype=float)
>>> x = spsolve(A, B)
>>> np.allclose(A.dot(x).todense(), B.todense())
True
"""
if not (isspmatrix_csc(A) or isspmatrix_csr(A)):
A = csc_matrix(A)
warn('spsolve requires A be CSC or CSR matrix format',
SparseEfficiencyWarning)
# b is a vector only if b have shape (n,) or (n, 1)
b_is_sparse = isspmatrix(b)
if not b_is_sparse:
b = asarray(b)
b_is_vector = ((b.ndim == 1) or (b.ndim == 2 and b.shape[1] == 1))
A.sort_indices()
A = A.asfptype() # upcast to a floating point format
result_dtype = np.promote_types(A.dtype, b.dtype)
if A.dtype != result_dtype:
A = A.astype(result_dtype)
if b.dtype != result_dtype:
b = b.astype(result_dtype)
# validate input shapes
M, N = A.shape
if (M != N):
raise ValueError("matrix must be square (has shape %s)" % ((M, N),))
if M != b.shape[0]:
raise ValueError("matrix - rhs dimension mismatch (%s - %s)"
% (A.shape, b.shape[0]))
use_umfpack = use_umfpack and useUmfpack
if b_is_vector and use_umfpack:
if b_is_sparse:
b_vec = b.toarray()
else:
b_vec = b
b_vec = asarray(b_vec, dtype=A.dtype).ravel()
if noScikit:
raise RuntimeError('Scikits.umfpack not installed.')
if A.dtype.char not in 'dD':
raise ValueError("convert matrix data to double, please, using"
" .astype(), or set linsolve.useUmfpack = False")
umf = umfpack.UmfpackContext(_get_umf_family(A))
x = umf.linsolve(umfpack.UMFPACK_A, A, b_vec,
autoTranspose=True)
else:
if b_is_vector and b_is_sparse:
b = b.toarray()
b_is_sparse = False
if not b_is_sparse:
if isspmatrix_csc(A):
flag = 1 # CSC format
else:
flag = 0 # CSR format
options = dict(ColPerm=permc_spec)
x, info = _superlu.gssv(N, A.nnz, A.data, A.indices, A.indptr,
b, flag, options=options)
if info != 0:
warn("Matrix is exactly singular", MatrixRankWarning)
x.fill(np.nan)
if b_is_vector:
x = x.ravel()
else:
# b is sparse
Afactsolve = factorized(A)
if not isspmatrix_csc(b):
warn('spsolve is more efficient when sparse b '
'is in the CSC matrix format', SparseEfficiencyWarning)
b = csc_matrix(b)
# Create a sparse output matrix by repeatedly applying
# the sparse factorization to solve columns of b.
data_segs = []
row_segs = []
col_segs = []
for j in range(b.shape[1]):
bj = b[:, j].A.ravel()
xj = Afactsolve(bj)
w = np.flatnonzero(xj)
segment_length = w.shape[0]
row_segs.append(w)
col_segs.append(np.ones(segment_length, dtype=int)*j)
data_segs.append(np.asarray(xj[w], dtype=A.dtype))
sparse_data = np.concatenate(data_segs)
sparse_row = np.concatenate(row_segs)
sparse_col = np.concatenate(col_segs)
x = A.__class__((sparse_data, (sparse_row, sparse_col)),
shape=b.shape, dtype=A.dtype)
return x
def splu(A, permc_spec=None, diag_pivot_thresh=None,
relax=None, panel_size=None, options=dict()):
"""
Compute the LU decomposition of a sparse, square matrix.
Parameters
----------
A : sparse matrix
Sparse matrix to factorize. Should be in CSR or CSC format.
permc_spec : str, optional
How to permute the columns of the matrix for sparsity preservation.
(default: 'COLAMD')
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering
diag_pivot_thresh : float, optional
Threshold used for a diagonal entry to be an acceptable pivot.
See SuperLU user's guide for details [1]_
relax : int, optional
Expert option for customizing the degree of relaxing supernodes.
See SuperLU user's guide for details [1]_
panel_size : int, optional
Expert option for customizing the panel size.
See SuperLU user's guide for details [1]_
options : dict, optional
Dictionary containing additional expert options to SuperLU.
See SuperLU user guide [1]_ (section 2.4 on the 'Options' argument)
for more details. For example, you can specify
``options=dict(Equil=False, IterRefine='SINGLE'))``
to turn equilibration off and perform a single iterative refinement.
Returns
-------
invA : scipy.sparse.linalg.SuperLU
Object, which has a ``solve`` method.
See also
--------
spilu : incomplete LU decomposition
Notes
-----
This function uses the SuperLU library.
References
----------
.. [1] SuperLU http://crd.lbl.gov/~xiaoye/SuperLU/
Examples
--------
>>> from scipy.sparse import csc_matrix
>>> from scipy.sparse.linalg import splu
>>> A = csc_matrix([[1., 0., 0.], [5., 0., 2.], [0., -1., 0.]], dtype=float)
>>> B = splu(A)
>>> x = np.array([1., 2., 3.], dtype=float)
>>> B.solve(x)
array([ 1. , -3. , -1.5])
>>> A.dot(B.solve(x))
array([ 1., 2., 3.])
>>> B.solve(A.dot(x))
array([ 1., 2., 3.])
"""
if not isspmatrix_csc(A):
A = csc_matrix(A)
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
A.sort_indices()
A = A.asfptype() # upcast to a floating point format
M, N = A.shape
if (M != N):
raise ValueError("can only factor square matrices") # is this true?
_options = dict(DiagPivotThresh=diag_pivot_thresh, ColPerm=permc_spec,
PanelSize=panel_size, Relax=relax)
if options is not None:
_options.update(options)
return _superlu.gstrf(N, A.nnz, A.data, A.indices, A.indptr,
ilu=False, options=_options)
def spilu(A, drop_tol=None, fill_factor=None, drop_rule=None, permc_spec=None,
diag_pivot_thresh=None, relax=None, panel_size=None, options=None):
"""
Compute an incomplete LU decomposition for a sparse, square matrix.
The resulting object is an approximation to the inverse of `A`.
Parameters
----------
A : (N, N) array_like
Sparse matrix to factorize
drop_tol : float, optional
Drop tolerance (0 <= tol <= 1) for an incomplete LU decomposition.
(default: 1e-4)
fill_factor : float, optional
Specifies the fill ratio upper bound (>= 1.0) for ILU. (default: 10)
drop_rule : str, optional
Comma-separated string of drop rules to use.
Available rules: ``basic``, ``prows``, ``column``, ``area``,
``secondary``, ``dynamic``, ``interp``. (Default: ``basic,area``)
See SuperLU documentation for details.
Remaining other options
Same as for `splu`
Returns
-------
invA_approx : scipy.sparse.linalg.SuperLU
Object, which has a ``solve`` method.
See also
--------
splu : complete LU decomposition
Notes
-----
To improve the better approximation to the inverse, you may need to
increase `fill_factor` AND decrease `drop_tol`.
This function uses the SuperLU library.
Examples
--------
>>> from scipy.sparse import csc_matrix
>>> from scipy.sparse.linalg import spilu
>>> A = csc_matrix([[1., 0., 0.], [5., 0., 2.], [0., -1., 0.]], dtype=float)
>>> B = spilu(A)
>>> x = np.array([1., 2., 3.], dtype=float)
>>> B.solve(x)
array([ 1. , -3. , -1.5])
>>> A.dot(B.solve(x))
array([ 1., 2., 3.])
>>> B.solve(A.dot(x))
array([ 1., 2., 3.])
"""
if not isspmatrix_csc(A):
A = csc_matrix(A)
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
A.sort_indices()
A = A.asfptype() # upcast to a floating point format
M, N = A.shape
if (M != N):
raise ValueError("can only factor square matrices") # is this true?
_options = dict(ILU_DropRule=drop_rule, ILU_DropTol=drop_tol,
ILU_FillFactor=fill_factor,
DiagPivotThresh=diag_pivot_thresh, ColPerm=permc_spec,
PanelSize=panel_size, Relax=relax)
if options is not None:
_options.update(options)
return _superlu.gstrf(N, A.nnz, A.data, A.indices, A.indptr,
ilu=True, options=_options)
def factorized(A):
"""
Return a function for solving a sparse linear system, with A pre-factorized.
Parameters
----------
A : (N, N) array_like
Input.
Returns
-------
solve : callable
To solve the linear system of equations given in `A`, the `solve`
callable should be passed an ndarray of shape (N,).
Examples
--------
>>> from scipy.sparse.linalg import factorized
>>> A = np.array([[ 3. , 2. , -1. ],
... [ 2. , -2. , 4. ],
... [-1. , 0.5, -1. ]])
>>> solve = factorized(A) # Makes LU decomposition.
>>> rhs1 = np.array([1, -2, 0])
>>> solve(rhs1) # Uses the LU factors.
array([ 1., -2., -2.])
"""
if useUmfpack:
if noScikit:
raise RuntimeError('Scikits.umfpack not installed.')
if not isspmatrix_csc(A):
A = csc_matrix(A)
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
A = A.asfptype() # upcast to a floating point format
if A.dtype.char not in 'dD':
raise ValueError("convert matrix data to double, please, using"
" .astype(), or set linsolve.useUmfpack = False")
umf = umfpack.UmfpackContext(_get_umf_family(A))
# Make LU decomposition.
umf.numeric(A)
def solve(b):
return umf.solve(umfpack.UMFPACK_A, A, b, autoTranspose=True)
return solve
else:
return splu(A).solve
def spsolve_triangular(A, b, lower=True, overwrite_A=False, overwrite_b=False):
"""
Solve the equation `A x = b` for `x`, assuming A is a triangular matrix.
Parameters
----------
A : (M, M) sparse matrix
A sparse square triangular matrix. Should be in CSR format.
b : (M,) or (M, N) array_like
Right-hand side matrix in `A x = b`
lower : bool, optional
Whether `A` is a lower or upper triangular matrix.
Default is lower triangular matrix.
overwrite_A : bool, optional
Allow changing `A`. The indices of `A` are going to be sorted and zero
entries are going to be removed.
Enabling gives a performance gain. Default is False.
overwrite_b : bool, optional
Allow overwriting data in `b`.
Enabling gives a performance gain. Default is False.
If `overwrite_b` is True, it should be ensured that
`b` has an appropriate dtype to be able to store the result.
Returns
-------
x : (M,) or (M, N) ndarray
Solution to the system `A x = b`. Shape of return matches shape of `b`.
Raises
------
LinAlgError
If `A` is singular or not triangular.
ValueError
If shape of `A` or shape of `b` do not match the requirements.
Notes
-----
.. versionadded:: 0.19.0
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.linalg import spsolve_triangular
>>> A = csr_matrix([[3, 0, 0], [1, -1, 0], [2, 0, 1]], dtype=float)
>>> B = np.array([[2, 0], [-1, 0], [2, 0]], dtype=float)
>>> x = spsolve_triangular(A, B)
>>> np.allclose(A.dot(x), B)
True
"""
# Check the input for correct type and format.
if not isspmatrix_csr(A):
warn('CSR matrix format is required. Converting to CSR matrix.',
SparseEfficiencyWarning)
A = csr_matrix(A)
elif not overwrite_A:
A = A.copy()
if A.shape[0] != A.shape[1]:
raise ValueError(
'A must be a square matrix but its shape is {}.'.format(A.shape))
A.eliminate_zeros()
A.sort_indices()
b = np.asanyarray(b)
if b.ndim not in [1, 2]:
raise ValueError(
'b must have 1 or 2 dims but its shape is {}.'.format(b.shape))
if A.shape[0] != b.shape[0]:
raise ValueError(
'The size of the dimensions of A must be equal to '
'the size of the first dimension of b but the shape of A is '
'{} and the shape of b is {}.'.format(A.shape, b.shape))
# Init x as (a copy of) b.
x_dtype = np.result_type(A.data, b, np.float)
if overwrite_b:
if np.can_cast(b.dtype, x_dtype, casting='same_kind'):
x = b
else:
raise ValueError(
'Cannot overwrite b (dtype {}) with result '
'of type {}.'.format(b.dtype, x_dtype))
else:
x = b.astype(x_dtype, copy=True)
# Choose forward or backward order.
if lower:
row_indices = range(len(b))
else:
row_indices = range(len(b) - 1, -1, -1)
# Fill x iteratively.
for i in row_indices:
# Get indices for i-th row.
indptr_start = A.indptr[i]
indptr_stop = A.indptr[i + 1]
if lower:
A_diagonal_index_row_i = indptr_stop - 1
A_off_diagonal_indices_row_i = slice(indptr_start, indptr_stop - 1)
else:
A_diagonal_index_row_i = indptr_start
A_off_diagonal_indices_row_i = slice(indptr_start + 1, indptr_stop)
# Check regularity and triangularity of A.
if indptr_stop <= indptr_start or A.indices[A_diagonal_index_row_i] < i:
raise LinAlgError(
'A is singular: diagonal {} is zero.'.format(i))
if A.indices[A_diagonal_index_row_i] > i:
raise LinAlgError(
'A is not triangular: A[{}, {}] is nonzero.'
''.format(i, A.indices[A_diagonal_index_row_i]))
# Incorporate off-diagonal entries.
A_column_indices_in_row_i = A.indices[A_off_diagonal_indices_row_i]
A_values_in_row_i = A.data[A_off_diagonal_indices_row_i]
x[i] -= np.dot(x[A_column_indices_in_row_i].T, A_values_in_row_i)
# Compute i-th entry of x.
x[i] /= A.data[A_diagonal_index_row_i]
return x
| 19,106 | 32.639085 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/dsolve/_add_newdocs.py
|
from numpy.lib import add_newdoc
add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU',
"""
LU factorization of a sparse matrix.
Factorization is represented as::
Pr * A * Pc = L * U
To construct these `SuperLU` objects, call the `splu` and `spilu`
functions.
Attributes
----------
shape
nnz
perm_c
perm_r
L
U
Methods
-------
solve
Notes
-----
.. versionadded:: 0.14.0
Examples
--------
The LU decomposition can be used to solve matrix equations. Consider:
>>> import numpy as np
>>> from scipy.sparse import csc_matrix, linalg as sla
>>> A = csc_matrix([[1,2,0,4],[1,0,0,1],[1,0,2,1],[2,2,1,0.]])
This can be solved for a given right-hand side:
>>> lu = sla.splu(A)
>>> b = np.array([1, 2, 3, 4])
>>> x = lu.solve(b)
>>> A.dot(x)
array([ 1., 2., 3., 4.])
The ``lu`` object also contains an explicit representation of the
decomposition. The permutations are represented as mappings of
indices:
>>> lu.perm_r
array([0, 2, 1, 3], dtype=int32)
>>> lu.perm_c
array([2, 0, 1, 3], dtype=int32)
The L and U factors are sparse matrices in CSC format:
>>> lu.L.A
array([[ 1. , 0. , 0. , 0. ],
[ 0. , 1. , 0. , 0. ],
[ 0. , 0. , 1. , 0. ],
[ 1. , 0.5, 0.5, 1. ]])
>>> lu.U.A
array([[ 2., 0., 1., 4.],
[ 0., 2., 1., 1.],
[ 0., 0., 1., 1.],
[ 0., 0., 0., -5.]])
The permutation matrices can be constructed:
>>> Pr = csc_matrix((4, 4))
>>> Pr[lu.perm_r, np.arange(4)] = 1
>>> Pc = csc_matrix((4, 4))
>>> Pc[np.arange(4), lu.perm_c] = 1
We can reassemble the original matrix:
>>> (Pr.T * (lu.L * lu.U) * Pc.T).A
array([[ 1., 2., 0., 4.],
[ 1., 0., 0., 1.],
[ 1., 0., 2., 1.],
[ 2., 2., 1., 0.]])
""")
add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('solve',
"""
solve(rhs[, trans])
Solves linear system of equations with one or several right-hand sides.
Parameters
----------
rhs : ndarray, shape (n,) or (n, k)
Right hand side(s) of equation
trans : {'N', 'T', 'H'}, optional
Type of system to solve::
'N': A * x == rhs (default)
'T': A^T * x == rhs
'H': A^H * x == rhs
i.e., normal, transposed, and hermitian conjugate.
Returns
-------
x : ndarray, shape ``rhs.shape``
Solution vector(s)
"""))
add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('L',
"""
Lower triangular factor with unit diagonal as a
`scipy.sparse.csc_matrix`.
.. versionadded:: 0.14.0
"""))
add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('U',
"""
Upper triangular factor as a `scipy.sparse.csc_matrix`.
.. versionadded:: 0.14.0
"""))
add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('shape',
"""
Shape of the original matrix as a tuple of ints.
"""))
add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('nnz',
"""
Number of nonzero elements in the matrix.
"""))
add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('perm_c',
"""
Permutation Pc represented as an array of indices.
The column permutation matrix can be reconstructed via:
>>> Pc = np.zeros((n, n))
>>> Pc[np.arange(n), perm_c] = 1
"""))
add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('perm_r',
"""
Permutation Pr represented as an array of indices.
The row permutation matrix can be reconstructed via:
>>> Pr = np.zeros((n, n))
>>> Pr[perm_r, np.arange(n)] = 1
"""))
| 3,801 | 23.529032 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/dsolve/__init__.py
|
"""
Linear Solvers
==============
The default solver is SuperLU (included in the scipy distribution),
which can solve real or complex linear systems in both single and
double precisions. It is automatically replaced by UMFPACK, if
available. Note that UMFPACK works in double precision only, so
switch it off by::
>>> use_solver(useUmfpack=False)
to solve in the single precision. See also use_solver documentation.
Example session::
>>> from scipy.sparse import csc_matrix, spdiags
>>> from numpy import array
>>> from scipy.sparse.linalg import spsolve, use_solver
>>>
>>> print("Inverting a sparse linear system:")
>>> print("The sparse matrix (constructed from diagonals):")
>>> a = spdiags([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1], 5, 5)
>>> b = array([1, 2, 3, 4, 5])
>>> print("Solve: single precision complex:")
>>> use_solver( useUmfpack = False )
>>> a = a.astype('F')
>>> x = spsolve(a, b)
>>> print(x)
>>> print("Error: ", a*x-b)
>>>
>>> print("Solve: double precision complex:")
>>> use_solver( useUmfpack = True )
>>> a = a.astype('D')
>>> x = spsolve(a, b)
>>> print(x)
>>> print("Error: ", a*x-b)
>>>
>>> print("Solve: double precision:")
>>> a = a.astype('d')
>>> x = spsolve(a, b)
>>> print(x)
>>> print("Error: ", a*x-b)
>>>
>>> print("Solve: single precision:")
>>> use_solver( useUmfpack = False )
>>> a = a.astype('f')
>>> x = spsolve(a, b.astype('f'))
>>> print(x)
>>> print("Error: ", a*x-b)
"""
from __future__ import division, print_function, absolute_import
#import umfpack
#__doc__ = '\n\n'.join( (__doc__, umfpack.__doc__) )
#del umfpack
from .linsolve import *
from ._superlu import SuperLU
from . import _add_newdocs
__all__ = [s for s in dir() if not s.startswith('_')]
from scipy._lib._testutils import PytestTester
test = PytestTester(__name__)
del PytestTester
| 1,953 | 27.318841 | 70 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/dsolve/tests/test_linsolve.py
|
from __future__ import division, print_function, absolute_import
import sys
import threading
import numpy as np
from numpy import array, finfo, arange, eye, all, unique, ones, dot, matrix
import numpy.random as random
from numpy.testing import (
assert_array_almost_equal, assert_almost_equal,
assert_equal, assert_array_equal, assert_, assert_allclose,
assert_warns)
import pytest
from pytest import raises as assert_raises
import scipy.linalg
from scipy.linalg import norm, inv
from scipy.sparse import (spdiags, SparseEfficiencyWarning, csc_matrix,
csr_matrix, identity, isspmatrix, dok_matrix, lil_matrix, bsr_matrix)
from scipy.sparse.linalg import SuperLU
from scipy.sparse.linalg.dsolve import (spsolve, use_solver, splu, spilu,
MatrixRankWarning, _superlu, spsolve_triangular, factorized)
from scipy._lib._numpy_compat import suppress_warnings
sup_sparse_efficiency = suppress_warnings()
sup_sparse_efficiency.filter(SparseEfficiencyWarning)
# scikits.umfpack is not a SciPy dependency but it is optionally used in
# dsolve, so check whether it's available
try:
import scikits.umfpack as umfpack
has_umfpack = True
except ImportError:
has_umfpack = False
def toarray(a):
if isspmatrix(a):
return a.toarray()
else:
return a
class TestFactorized(object):
def setup_method(self):
n = 5
d = arange(n) + 1
self.n = n
self.A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n).tocsc()
random.seed(1234)
def _check_singular(self):
A = csc_matrix((5,5), dtype='d')
b = ones(5)
assert_array_almost_equal(0. * b, factorized(A)(b))
def _check_non_singular(self):
# Make a diagonal dominant, to make sure it is not singular
n = 5
a = csc_matrix(random.rand(n, n))
b = ones(n)
expected = splu(a).solve(b)
assert_array_almost_equal(factorized(a)(b), expected)
def test_singular_without_umfpack(self):
use_solver(useUmfpack=False)
with assert_raises(RuntimeError, message="Factor is exactly singular"):
self._check_singular()
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_singular_with_umfpack(self):
use_solver(useUmfpack=True)
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "divide by zero encountered in double_scalars")
assert_warns(umfpack.UmfpackWarning, self._check_singular)
def test_non_singular_without_umfpack(self):
use_solver(useUmfpack=False)
self._check_non_singular()
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_non_singular_with_umfpack(self):
use_solver(useUmfpack=True)
self._check_non_singular()
def test_cannot_factorize_nonsquare_matrix_without_umfpack(self):
use_solver(useUmfpack=False)
msg = "can only factor square matrices"
with assert_raises(ValueError, message=msg):
factorized(self.A[:, :4])
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_factorizes_nonsquare_matrix_with_umfpack(self):
use_solver(useUmfpack=True)
# does not raise
factorized(self.A[:,:4])
def test_call_with_incorrectly_sized_matrix_without_umfpack(self):
use_solver(useUmfpack=False)
solve = factorized(self.A)
b = random.rand(4)
B = random.rand(4, 3)
BB = random.rand(self.n, 3, 9)
with assert_raises(ValueError, message="is of incompatible size"):
solve(b)
with assert_raises(ValueError, message="is of incompatible size"):
solve(B)
with assert_raises(ValueError,
message="object too deep for desired array"):
solve(BB)
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_call_with_incorrectly_sized_matrix_with_umfpack(self):
use_solver(useUmfpack=True)
solve = factorized(self.A)
b = random.rand(4)
B = random.rand(4, 3)
BB = random.rand(self.n, 3, 9)
# does not raise
solve(b)
msg = "object too deep for desired array"
with assert_raises(ValueError, message=msg):
solve(B)
with assert_raises(ValueError, message=msg):
solve(BB)
def test_call_with_cast_to_complex_without_umfpack(self):
use_solver(useUmfpack=False)
solve = factorized(self.A)
b = random.rand(4)
for t in [np.complex64, np.complex128]:
with assert_raises(TypeError, message="Cannot cast array data"):
solve(b.astype(t))
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_call_with_cast_to_complex_with_umfpack(self):
use_solver(useUmfpack=True)
solve = factorized(self.A)
b = random.rand(4)
for t in [np.complex64, np.complex128]:
assert_warns(np.ComplexWarning, solve, b.astype(t))
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_assume_sorted_indices_flag(self):
# a sparse matrix with unsorted indices
unsorted_inds = np.array([2, 0, 1, 0])
data = np.array([10, 16, 5, 0.4])
indptr = np.array([0, 1, 2, 4])
A = csc_matrix((data, unsorted_inds, indptr), (3, 3))
b = ones(3)
# should raise when incorrectly assuming indices are sorted
use_solver(useUmfpack=True, assumeSortedIndices=True)
with assert_raises(RuntimeError,
message="UMFPACK_ERROR_invalid_matrix"):
factorized(A)
# should sort indices and succeed when not assuming indices are sorted
use_solver(useUmfpack=True, assumeSortedIndices=False)
expected = splu(A.copy()).solve(b)
assert_equal(A.has_sorted_indices, 0)
assert_array_almost_equal(factorized(A)(b), expected)
assert_equal(A.has_sorted_indices, 1)
class TestLinsolve(object):
def setup_method(self):
use_solver(useUmfpack=False)
def test_singular(self):
A = csc_matrix((5,5), dtype='d')
b = array([1, 2, 3, 4, 5],dtype='d')
with suppress_warnings() as sup:
sup.filter(MatrixRankWarning, "Matrix is exactly singular")
x = spsolve(A, b)
assert_(not np.isfinite(x).any())
def test_singular_gh_3312(self):
# "Bad" test case that leads SuperLU to call LAPACK with invalid
# arguments. Check that it fails moderately gracefully.
ij = np.array([(17, 0), (17, 6), (17, 12), (10, 13)], dtype=np.int32)
v = np.array([0.284213, 0.94933781, 0.15767017, 0.38797296])
A = csc_matrix((v, ij.T), shape=(20, 20))
b = np.arange(20)
try:
# should either raise a runtimeerror or return value
# appropriate for singular input
x = spsolve(A, b)
assert_(not np.isfinite(x).any())
except RuntimeError:
pass
def test_twodiags(self):
A = spdiags([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1], 5, 5)
b = array([1, 2, 3, 4, 5])
# condition number of A
cond_A = norm(A.todense(),2) * norm(inv(A.todense()),2)
for t in ['f','d','F','D']:
eps = finfo(t).eps # floating point epsilon
b = b.astype(t)
for format in ['csc','csr']:
Asp = A.astype(t).asformat(format)
x = spsolve(Asp,b)
assert_(norm(b - Asp*x) < 10 * cond_A * eps)
def test_bvector_smoketest(self):
Adense = matrix([[0., 1., 1.],
[1., 0., 1.],
[0., 0., 1.]])
As = csc_matrix(Adense)
random.seed(1234)
x = random.randn(3)
b = As*x
x2 = spsolve(As, b)
assert_array_almost_equal(x, x2)
def test_bmatrix_smoketest(self):
Adense = matrix([[0., 1., 1.],
[1., 0., 1.],
[0., 0., 1.]])
As = csc_matrix(Adense)
random.seed(1234)
x = random.randn(3, 4)
Bdense = As.dot(x)
Bs = csc_matrix(Bdense)
x2 = spsolve(As, Bs)
assert_array_almost_equal(x, x2.todense())
@sup_sparse_efficiency
def test_non_square(self):
# A is not square.
A = ones((3, 4))
b = ones((4, 1))
assert_raises(ValueError, spsolve, A, b)
# A2 and b2 have incompatible shapes.
A2 = csc_matrix(eye(3))
b2 = array([1.0, 2.0])
assert_raises(ValueError, spsolve, A2, b2)
@sup_sparse_efficiency
def test_example_comparison(self):
row = array([0,0,1,2,2,2])
col = array([0,2,2,0,1,2])
data = array([1,2,3,-4,5,6])
sM = csr_matrix((data,(row,col)), shape=(3,3), dtype=float)
M = sM.todense()
row = array([0,0,1,1,0,0])
col = array([0,2,1,1,0,0])
data = array([1,1,1,1,1,1])
sN = csr_matrix((data, (row,col)), shape=(3,3), dtype=float)
N = sN.todense()
sX = spsolve(sM, sN)
X = scipy.linalg.solve(M, N)
assert_array_almost_equal(X, sX.todense())
@sup_sparse_efficiency
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_shape_compatibility(self):
use_solver(useUmfpack=True)
A = csc_matrix([[1., 0], [0, 2]])
bs = [
[1, 6],
array([1, 6]),
[[1], [6]],
array([[1], [6]]),
csc_matrix([[1], [6]]),
csr_matrix([[1], [6]]),
dok_matrix([[1], [6]]),
bsr_matrix([[1], [6]]),
array([[1., 2., 3.], [6., 8., 10.]]),
csc_matrix([[1., 2., 3.], [6., 8., 10.]]),
csr_matrix([[1., 2., 3.], [6., 8., 10.]]),
dok_matrix([[1., 2., 3.], [6., 8., 10.]]),
bsr_matrix([[1., 2., 3.], [6., 8., 10.]]),
]
for b in bs:
x = np.linalg.solve(A.toarray(), toarray(b))
for spmattype in [csc_matrix, csr_matrix, dok_matrix, lil_matrix]:
x1 = spsolve(spmattype(A), b, use_umfpack=True)
x2 = spsolve(spmattype(A), b, use_umfpack=False)
# check solution
if x.ndim == 2 and x.shape[1] == 1:
# interprets also these as "vectors"
x = x.ravel()
assert_array_almost_equal(toarray(x1), x, err_msg=repr((b, spmattype, 1)))
assert_array_almost_equal(toarray(x2), x, err_msg=repr((b, spmattype, 2)))
# dense vs. sparse output ("vectors" are always dense)
if isspmatrix(b) and x.ndim > 1:
assert_(isspmatrix(x1), repr((b, spmattype, 1)))
assert_(isspmatrix(x2), repr((b, spmattype, 2)))
else:
assert_(isinstance(x1, np.ndarray), repr((b, spmattype, 1)))
assert_(isinstance(x2, np.ndarray), repr((b, spmattype, 2)))
# check output shape
if x.ndim == 1:
# "vector"
assert_equal(x1.shape, (A.shape[1],))
assert_equal(x2.shape, (A.shape[1],))
else:
# "matrix"
assert_equal(x1.shape, x.shape)
assert_equal(x2.shape, x.shape)
A = csc_matrix((3, 3))
b = csc_matrix((1, 3))
assert_raises(ValueError, spsolve, A, b)
@sup_sparse_efficiency
def test_ndarray_support(self):
A = array([[1., 2.], [2., 0.]])
x = array([[1., 1.], [0.5, -0.5]])
b = array([[2., 0.], [2., 2.]])
assert_array_almost_equal(x, spsolve(A, b))
def test_gssv_badinput(self):
N = 10
d = arange(N) + 1.0
A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), N, N)
for spmatrix in (csc_matrix, csr_matrix):
A = spmatrix(A)
b = np.arange(N)
def not_c_contig(x):
return x.repeat(2)[::2]
def not_1dim(x):
return x[:,None]
def bad_type(x):
return x.astype(bool)
def too_short(x):
return x[:-1]
badops = [not_c_contig, not_1dim, bad_type, too_short]
for badop in badops:
msg = "%r %r" % (spmatrix, badop)
# Not C-contiguous
assert_raises((ValueError, TypeError), _superlu.gssv,
N, A.nnz, badop(A.data), A.indices, A.indptr,
b, int(spmatrix == csc_matrix), err_msg=msg)
assert_raises((ValueError, TypeError), _superlu.gssv,
N, A.nnz, A.data, badop(A.indices), A.indptr,
b, int(spmatrix == csc_matrix), err_msg=msg)
assert_raises((ValueError, TypeError), _superlu.gssv,
N, A.nnz, A.data, A.indices, badop(A.indptr),
b, int(spmatrix == csc_matrix), err_msg=msg)
def test_sparsity_preservation(self):
ident = csc_matrix([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
b = csc_matrix([
[0, 1],
[1, 0],
[0, 0]])
x = spsolve(ident, b)
assert_equal(ident.nnz, 3)
assert_equal(b.nnz, 2)
assert_equal(x.nnz, 2)
assert_allclose(x.A, b.A, atol=1e-12, rtol=1e-12)
def test_dtype_cast(self):
A_real = scipy.sparse.csr_matrix([[1, 2, 0],
[0, 0, 3],
[4, 0, 5]])
A_complex = scipy.sparse.csr_matrix([[1, 2, 0],
[0, 0, 3],
[4, 0, 5 + 1j]])
b_real = np.array([1,1,1])
b_complex = np.array([1,1,1]) + 1j*np.array([1,1,1])
x = spsolve(A_real, b_real)
assert_(np.issubdtype(x.dtype, np.floating))
x = spsolve(A_real, b_complex)
assert_(np.issubdtype(x.dtype, np.complexfloating))
x = spsolve(A_complex, b_real)
assert_(np.issubdtype(x.dtype, np.complexfloating))
x = spsolve(A_complex, b_complex)
assert_(np.issubdtype(x.dtype, np.complexfloating))
class TestSplu(object):
def setup_method(self):
use_solver(useUmfpack=False)
n = 40
d = arange(n) + 1
self.n = n
self.A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n)
random.seed(1234)
def _smoketest(self, spxlu, check, dtype):
if np.issubdtype(dtype, np.complexfloating):
A = self.A + 1j*self.A.T
else:
A = self.A
A = A.astype(dtype)
lu = spxlu(A)
rng = random.RandomState(1234)
# Input shapes
for k in [None, 1, 2, self.n, self.n+2]:
msg = "k=%r" % (k,)
if k is None:
b = rng.rand(self.n)
else:
b = rng.rand(self.n, k)
if np.issubdtype(dtype, np.complexfloating):
b = b + 1j*rng.rand(*b.shape)
b = b.astype(dtype)
x = lu.solve(b)
check(A, b, x, msg)
x = lu.solve(b, 'T')
check(A.T, b, x, msg)
x = lu.solve(b, 'H')
check(A.T.conj(), b, x, msg)
@sup_sparse_efficiency
def test_splu_smoketest(self):
self._internal_test_splu_smoketest()
def _internal_test_splu_smoketest(self):
# Check that splu works at all
def check(A, b, x, msg=""):
eps = np.finfo(A.dtype).eps
r = A * x
assert_(abs(r - b).max() < 1e3*eps, msg)
self._smoketest(splu, check, np.float32)
self._smoketest(splu, check, np.float64)
self._smoketest(splu, check, np.complex64)
self._smoketest(splu, check, np.complex128)
@sup_sparse_efficiency
def test_spilu_smoketest(self):
self._internal_test_spilu_smoketest()
def _internal_test_spilu_smoketest(self):
errors = []
def check(A, b, x, msg=""):
r = A * x
err = abs(r - b).max()
assert_(err < 1e-2, msg)
if b.dtype in (np.float64, np.complex128):
errors.append(err)
self._smoketest(spilu, check, np.float32)
self._smoketest(spilu, check, np.float64)
self._smoketest(spilu, check, np.complex64)
self._smoketest(spilu, check, np.complex128)
assert_(max(errors) > 1e-5)
@sup_sparse_efficiency
def test_spilu_drop_rule(self):
# Test passing in the drop_rule argument to spilu.
A = identity(2)
rules = [
b'basic,area'.decode('ascii'), # unicode
b'basic,area', # ascii
[b'basic', b'area'.decode('ascii')]
]
for rule in rules:
# Argument should be accepted
assert_(isinstance(spilu(A, drop_rule=rule), SuperLU))
def test_splu_nnz0(self):
A = csc_matrix((5,5), dtype='d')
assert_raises(RuntimeError, splu, A)
def test_spilu_nnz0(self):
A = csc_matrix((5,5), dtype='d')
assert_raises(RuntimeError, spilu, A)
def test_splu_basic(self):
# Test basic splu functionality.
n = 30
rng = random.RandomState(12)
a = rng.rand(n, n)
a[a < 0.95] = 0
# First test with a singular matrix
a[:, 0] = 0
a_ = csc_matrix(a)
# Matrix is exactly singular
assert_raises(RuntimeError, splu, a_)
# Make a diagonal dominant, to make sure it is not singular
a += 4*eye(n)
a_ = csc_matrix(a)
lu = splu(a_)
b = ones(n)
x = lu.solve(b)
assert_almost_equal(dot(a, x), b)
def test_splu_perm(self):
# Test the permutation vectors exposed by splu.
n = 30
a = random.random((n, n))
a[a < 0.95] = 0
# Make a diagonal dominant, to make sure it is not singular
a += 4*eye(n)
a_ = csc_matrix(a)
lu = splu(a_)
# Check that the permutation indices do belong to [0, n-1].
for perm in (lu.perm_r, lu.perm_c):
assert_(all(perm > -1))
assert_(all(perm < n))
assert_equal(len(unique(perm)), len(perm))
# Now make a symmetric, and test that the two permutation vectors are
# the same
# Note: a += a.T relies on undefined behavior.
a = a + a.T
a_ = csc_matrix(a)
lu = splu(a_)
assert_array_equal(lu.perm_r, lu.perm_c)
@pytest.mark.skipif(not hasattr(sys, 'getrefcount'), reason="no sys.getrefcount")
def test_lu_refcount(self):
# Test that we are keeping track of the reference count with splu.
n = 30
a = random.random((n, n))
a[a < 0.95] = 0
# Make a diagonal dominant, to make sure it is not singular
a += 4*eye(n)
a_ = csc_matrix(a)
lu = splu(a_)
# And now test that we don't have a refcount bug
rc = sys.getrefcount(lu)
for attr in ('perm_r', 'perm_c'):
perm = getattr(lu, attr)
assert_equal(sys.getrefcount(lu), rc + 1)
del perm
assert_equal(sys.getrefcount(lu), rc)
def test_bad_inputs(self):
A = self.A.tocsc()
assert_raises(ValueError, splu, A[:,:4])
assert_raises(ValueError, spilu, A[:,:4])
for lu in [splu(A), spilu(A)]:
b = random.rand(42)
B = random.rand(42, 3)
BB = random.rand(self.n, 3, 9)
assert_raises(ValueError, lu.solve, b)
assert_raises(ValueError, lu.solve, B)
assert_raises(ValueError, lu.solve, BB)
assert_raises(TypeError, lu.solve,
b.astype(np.complex64))
assert_raises(TypeError, lu.solve,
b.astype(np.complex128))
@sup_sparse_efficiency
def test_superlu_dlamch_i386_nan(self):
# SuperLU 4.3 calls some functions returning floats without
# declaring them. On i386@linux call convention, this fails to
# clear floating point registers after call. As a result, NaN
# can appear in the next floating point operation made.
#
# Here's a test case that triggered the issue.
n = 8
d = np.arange(n) + 1
A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n)
A = A.astype(np.float32)
spilu(A)
A = A + 1j*A
B = A.A
assert_(not np.isnan(B).any())
@sup_sparse_efficiency
def test_lu_attr(self):
def check(dtype, complex_2=False):
A = self.A.astype(dtype)
if complex_2:
A = A + 1j*A.T
n = A.shape[0]
lu = splu(A)
# Check that the decomposition is as advertized
Pc = np.zeros((n, n))
Pc[np.arange(n), lu.perm_c] = 1
Pr = np.zeros((n, n))
Pr[lu.perm_r, np.arange(n)] = 1
Ad = A.toarray()
lhs = Pr.dot(Ad).dot(Pc)
rhs = (lu.L * lu.U).toarray()
eps = np.finfo(dtype).eps
assert_allclose(lhs, rhs, atol=100*eps)
check(np.float32)
check(np.float64)
check(np.complex64)
check(np.complex128)
check(np.complex64, True)
check(np.complex128, True)
@sup_sparse_efficiency
def test_threads_parallel(self):
oks = []
def worker():
try:
self.test_splu_basic()
self._internal_test_splu_smoketest()
self._internal_test_spilu_smoketest()
oks.append(True)
except:
pass
threads = [threading.Thread(target=worker)
for k in range(20)]
for t in threads:
t.start()
for t in threads:
t.join()
assert_equal(len(oks), 20)
class TestSpsolveTriangular(object):
def setup_method(self):
use_solver(useUmfpack=False)
def test_singular(self):
n = 5
A = csr_matrix((n, n))
b = np.arange(n)
for lower in (True, False):
assert_raises(scipy.linalg.LinAlgError, spsolve_triangular, A, b, lower=lower)
@sup_sparse_efficiency
def test_bad_shape(self):
# A is not square.
A = np.zeros((3, 4))
b = ones((4, 1))
assert_raises(ValueError, spsolve_triangular, A, b)
# A2 and b2 have incompatible shapes.
A2 = csr_matrix(eye(3))
b2 = array([1.0, 2.0])
assert_raises(ValueError, spsolve_triangular, A2, b2)
@sup_sparse_efficiency
def test_input_types(self):
A = array([[1., 0.], [1., 2.]])
b = array([[2., 0.], [2., 2.]])
for matrix_type in (array, csc_matrix, csr_matrix):
x = spsolve_triangular(matrix_type(A), b, lower=True)
assert_array_almost_equal(A.dot(x), b)
@sup_sparse_efficiency
def test_random(self):
def random_triangle_matrix(n, lower=True):
A = scipy.sparse.random(n, n, density=0.1, format='coo')
if lower:
A = scipy.sparse.tril(A)
else:
A = scipy.sparse.triu(A)
A = A.tocsr(copy=False)
for i in range(n):
A[i, i] = np.random.rand() + 1
return A
np.random.seed(1234)
for lower in (True, False):
for n in (10, 10**2, 10**3):
A = random_triangle_matrix(n, lower=lower)
for m in (1, 10):
for b in (np.random.rand(n, m),
np.random.randint(-9, 9, (n, m)),
np.random.randint(-9, 9, (n, m)) +
np.random.randint(-9, 9, (n, m)) * 1j):
x = spsolve_triangular(A, b, lower=lower)
assert_array_almost_equal(A.dot(x), b)
| 24,273 | 32.854951 | 90 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/sparse/linalg/dsolve/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/mmio.py
|
"""
Matrix Market I/O in Python.
See http://math.nist.gov/MatrixMarket/formats.html
for information about the Matrix Market format.
"""
#
# Author: Pearu Peterson <pearu@cens.ioc.ee>
# Created: October, 2004
#
# References:
# http://math.nist.gov/MatrixMarket/
#
from __future__ import division, print_function, absolute_import
import os
import sys
from numpy import (asarray, real, imag, conj, zeros, ndarray, concatenate,
ones, ascontiguousarray, vstack, savetxt, fromfile,
fromstring, can_cast)
from numpy.compat import asbytes, asstr
from scipy._lib.six import string_types
from scipy.sparse import coo_matrix, isspmatrix
__all__ = ['mminfo', 'mmread', 'mmwrite', 'MMFile']
# -----------------------------------------------------------------------------
def mminfo(source):
"""
Return size and storage parameters from Matrix Market file-like 'source'.
Parameters
----------
source : str or file-like
Matrix Market filename (extension .mtx) or open file-like object
Returns
-------
rows : int
Number of matrix rows.
cols : int
Number of matrix columns.
entries : int
Number of non-zero entries of a sparse matrix
or rows*cols for a dense matrix.
format : str
Either 'coordinate' or 'array'.
field : str
Either 'real', 'complex', 'pattern', or 'integer'.
symmetry : str
Either 'general', 'symmetric', 'skew-symmetric', or 'hermitian'.
"""
return MMFile.info(source)
# -----------------------------------------------------------------------------
def mmread(source):
"""
Reads the contents of a Matrix Market file-like 'source' into a matrix.
Parameters
----------
source : str or file-like
Matrix Market filename (extensions .mtx, .mtz.gz)
or open file-like object.
Returns
-------
a : ndarray or coo_matrix
Dense or sparse matrix depending on the matrix format in the
Matrix Market file.
"""
return MMFile().read(source)
# -----------------------------------------------------------------------------
def mmwrite(target, a, comment='', field=None, precision=None, symmetry=None):
"""
Writes the sparse or dense array `a` to Matrix Market file-like `target`.
Parameters
----------
target : str or file-like
Matrix Market filename (extension .mtx) or open file-like object.
a : array like
Sparse or dense 2D array.
comment : str, optional
Comments to be prepended to the Matrix Market file.
field : None or str, optional
Either 'real', 'complex', 'pattern', or 'integer'.
precision : None or int, optional
Number of digits to display for real or complex values.
symmetry : None or str, optional
Either 'general', 'symmetric', 'skew-symmetric', or 'hermitian'.
If symmetry is None the symmetry type of 'a' is determined by its
values.
"""
MMFile().write(target, a, comment, field, precision, symmetry)
###############################################################################
class MMFile (object):
__slots__ = ('_rows',
'_cols',
'_entries',
'_format',
'_field',
'_symmetry')
@property
def rows(self):
return self._rows
@property
def cols(self):
return self._cols
@property
def entries(self):
return self._entries
@property
def format(self):
return self._format
@property
def field(self):
return self._field
@property
def symmetry(self):
return self._symmetry
@property
def has_symmetry(self):
return self._symmetry in (self.SYMMETRY_SYMMETRIC,
self.SYMMETRY_SKEW_SYMMETRIC,
self.SYMMETRY_HERMITIAN)
# format values
FORMAT_COORDINATE = 'coordinate'
FORMAT_ARRAY = 'array'
FORMAT_VALUES = (FORMAT_COORDINATE, FORMAT_ARRAY)
@classmethod
def _validate_format(self, format):
if format not in self.FORMAT_VALUES:
raise ValueError('unknown format type %s, must be one of %s' %
(format, self.FORMAT_VALUES))
# field values
FIELD_INTEGER = 'integer'
FIELD_UNSIGNED = 'unsigned-integer'
FIELD_REAL = 'real'
FIELD_COMPLEX = 'complex'
FIELD_PATTERN = 'pattern'
FIELD_VALUES = (FIELD_INTEGER, FIELD_UNSIGNED, FIELD_REAL, FIELD_COMPLEX, FIELD_PATTERN)
@classmethod
def _validate_field(self, field):
if field not in self.FIELD_VALUES:
raise ValueError('unknown field type %s, must be one of %s' %
(field, self.FIELD_VALUES))
# symmetry values
SYMMETRY_GENERAL = 'general'
SYMMETRY_SYMMETRIC = 'symmetric'
SYMMETRY_SKEW_SYMMETRIC = 'skew-symmetric'
SYMMETRY_HERMITIAN = 'hermitian'
SYMMETRY_VALUES = (SYMMETRY_GENERAL, SYMMETRY_SYMMETRIC,
SYMMETRY_SKEW_SYMMETRIC, SYMMETRY_HERMITIAN)
@classmethod
def _validate_symmetry(self, symmetry):
if symmetry not in self.SYMMETRY_VALUES:
raise ValueError('unknown symmetry type %s, must be one of %s' %
(symmetry, self.SYMMETRY_VALUES))
DTYPES_BY_FIELD = {FIELD_INTEGER: 'intp',
FIELD_UNSIGNED: 'uint64',
FIELD_REAL: 'd',
FIELD_COMPLEX: 'D',
FIELD_PATTERN: 'd'}
# -------------------------------------------------------------------------
@staticmethod
def reader():
pass
# -------------------------------------------------------------------------
@staticmethod
def writer():
pass
# -------------------------------------------------------------------------
@classmethod
def info(self, source):
"""
Return size, storage parameters from Matrix Market file-like 'source'.
Parameters
----------
source : str or file-like
Matrix Market filename (extension .mtx) or open file-like object
Returns
-------
rows : int
Number of matrix rows.
cols : int
Number of matrix columns.
entries : int
Number of non-zero entries of a sparse matrix
or rows*cols for a dense matrix.
format : str
Either 'coordinate' or 'array'.
field : str
Either 'real', 'complex', 'pattern', or 'integer'.
symmetry : str
Either 'general', 'symmetric', 'skew-symmetric', or 'hermitian'.
"""
stream, close_it = self._open(source)
try:
# read and validate header line
line = stream.readline()
mmid, matrix, format, field, symmetry = \
[asstr(part.strip()) for part in line.split()]
if not mmid.startswith('%%MatrixMarket'):
raise ValueError('source is not in Matrix Market format')
if not matrix.lower() == 'matrix':
raise ValueError("Problem reading file header: " + line)
# http://math.nist.gov/MatrixMarket/formats.html
if format.lower() == 'array':
format = self.FORMAT_ARRAY
elif format.lower() == 'coordinate':
format = self.FORMAT_COORDINATE
# skip comments
while line.startswith(b'%'):
line = stream.readline()
line = line.split()
if format == self.FORMAT_ARRAY:
if not len(line) == 2:
raise ValueError("Header line not of length 2: " + line)
rows, cols = map(int, line)
entries = rows * cols
else:
if not len(line) == 3:
raise ValueError("Header line not of length 3: " + line)
rows, cols, entries = map(int, line)
return (rows, cols, entries, format, field.lower(),
symmetry.lower())
finally:
if close_it:
stream.close()
# -------------------------------------------------------------------------
@staticmethod
def _open(filespec, mode='rb'):
""" Return an open file stream for reading based on source.
If source is a file name, open it (after trying to find it with mtx and
gzipped mtx extensions). Otherwise, just return source.
Parameters
----------
filespec : str or file-like
String giving file name or file-like object
mode : str, optional
Mode with which to open file, if `filespec` is a file name.
Returns
-------
fobj : file-like
Open file-like object.
close_it : bool
True if the calling function should close this file when done,
false otherwise.
"""
close_it = False
if isinstance(filespec, string_types):
close_it = True
# open for reading
if mode[0] == 'r':
# determine filename plus extension
if not os.path.isfile(filespec):
if os.path.isfile(filespec+'.mtx'):
filespec = filespec + '.mtx'
elif os.path.isfile(filespec+'.mtx.gz'):
filespec = filespec + '.mtx.gz'
elif os.path.isfile(filespec+'.mtx.bz2'):
filespec = filespec + '.mtx.bz2'
# open filename
if filespec.endswith('.gz'):
import gzip
stream = gzip.open(filespec, mode)
elif filespec.endswith('.bz2'):
import bz2
stream = bz2.BZ2File(filespec, 'rb')
else:
stream = open(filespec, mode)
# open for writing
else:
if filespec[-4:] != '.mtx':
filespec = filespec + '.mtx'
stream = open(filespec, mode)
else:
stream = filespec
return stream, close_it
# -------------------------------------------------------------------------
@staticmethod
def _get_symmetry(a):
m, n = a.shape
if m != n:
return MMFile.SYMMETRY_GENERAL
issymm = True
isskew = True
isherm = a.dtype.char in 'FD'
# sparse input
if isspmatrix(a):
# check if number of nonzero entries of lower and upper triangle
# matrix are equal
a = a.tocoo()
(row, col) = a.nonzero()
if (row < col).sum() != (row > col).sum():
return MMFile.SYMMETRY_GENERAL
# define iterator over symmetric pair entries
a = a.todok()
def symm_iterator():
for ((i, j), aij) in a.items():
if i > j:
aji = a[j, i]
yield (aij, aji)
# non-sparse input
else:
# define iterator over symmetric pair entries
def symm_iterator():
for j in range(n):
for i in range(j+1, n):
aij, aji = a[i][j], a[j][i]
yield (aij, aji)
# check for symmetry
for (aij, aji) in symm_iterator():
if issymm and aij != aji:
issymm = False
if isskew and aij != -aji:
isskew = False
if isherm and aij != conj(aji):
isherm = False
if not (issymm or isskew or isherm):
break
# return symmetry value
if issymm:
return MMFile.SYMMETRY_SYMMETRIC
if isskew:
return MMFile.SYMMETRY_SKEW_SYMMETRIC
if isherm:
return MMFile.SYMMETRY_HERMITIAN
return MMFile.SYMMETRY_GENERAL
# -------------------------------------------------------------------------
@staticmethod
def _field_template(field, precision):
return {MMFile.FIELD_REAL: '%%.%ie\n' % precision,
MMFile.FIELD_INTEGER: '%i\n',
MMFile.FIELD_UNSIGNED: '%u\n',
MMFile.FIELD_COMPLEX: '%%.%ie %%.%ie\n' %
(precision, precision)
}.get(field, None)
# -------------------------------------------------------------------------
def __init__(self, **kwargs):
self._init_attrs(**kwargs)
# -------------------------------------------------------------------------
def read(self, source):
"""
Reads the contents of a Matrix Market file-like 'source' into a matrix.
Parameters
----------
source : str or file-like
Matrix Market filename (extensions .mtx, .mtz.gz)
or open file object.
Returns
-------
a : ndarray or coo_matrix
Dense or sparse matrix depending on the matrix format in the
Matrix Market file.
"""
stream, close_it = self._open(source)
try:
self._parse_header(stream)
return self._parse_body(stream)
finally:
if close_it:
stream.close()
# -------------------------------------------------------------------------
def write(self, target, a, comment='', field=None, precision=None,
symmetry=None):
"""
Writes sparse or dense array `a` to Matrix Market file-like `target`.
Parameters
----------
target : str or file-like
Matrix Market filename (extension .mtx) or open file-like object.
a : array like
Sparse or dense 2D array.
comment : str, optional
Comments to be prepended to the Matrix Market file.
field : None or str, optional
Either 'real', 'complex', 'pattern', or 'integer'.
precision : None or int, optional
Number of digits to display for real or complex values.
symmetry : None or str, optional
Either 'general', 'symmetric', 'skew-symmetric', or 'hermitian'.
If symmetry is None the symmetry type of 'a' is determined by its
values.
"""
stream, close_it = self._open(target, 'wb')
try:
self._write(stream, a, comment, field, precision, symmetry)
finally:
if close_it:
stream.close()
else:
stream.flush()
# -------------------------------------------------------------------------
def _init_attrs(self, **kwargs):
"""
Initialize each attributes with the corresponding keyword arg value
or a default of None
"""
attrs = self.__class__.__slots__
public_attrs = [attr[1:] for attr in attrs]
invalid_keys = set(kwargs.keys()) - set(public_attrs)
if invalid_keys:
raise ValueError('''found %s invalid keyword arguments, please only
use %s''' % (tuple(invalid_keys),
public_attrs))
for attr in attrs:
setattr(self, attr, kwargs.get(attr[1:], None))
# -------------------------------------------------------------------------
def _parse_header(self, stream):
rows, cols, entries, format, field, symmetry = \
self.__class__.info(stream)
self._init_attrs(rows=rows, cols=cols, entries=entries, format=format,
field=field, symmetry=symmetry)
# -------------------------------------------------------------------------
def _parse_body(self, stream):
rows, cols, entries, format, field, symm = (self.rows, self.cols,
self.entries, self.format,
self.field, self.symmetry)
try:
from scipy.sparse import coo_matrix
except ImportError:
coo_matrix = None
dtype = self.DTYPES_BY_FIELD.get(field, None)
has_symmetry = self.has_symmetry
is_integer = field == self.FIELD_INTEGER
is_unsigned_integer = field == self.FIELD_UNSIGNED
is_complex = field == self.FIELD_COMPLEX
is_skew = symm == self.SYMMETRY_SKEW_SYMMETRIC
is_herm = symm == self.SYMMETRY_HERMITIAN
is_pattern = field == self.FIELD_PATTERN
if format == self.FORMAT_ARRAY:
a = zeros((rows, cols), dtype=dtype)
line = 1
i, j = 0, 0
if is_skew:
a[i, j] = 0
if i < rows - 1:
i += 1
while line:
line = stream.readline()
if not line or line.startswith(b'%'):
continue
if is_integer:
aij = int(line)
elif is_unsigned_integer:
aij = int(line)
elif is_complex:
aij = complex(*map(float, line.split()))
else:
aij = float(line)
a[i, j] = aij
if has_symmetry and i != j:
if is_skew:
a[j, i] = -aij
elif is_herm:
a[j, i] = conj(aij)
else:
a[j, i] = aij
if i < rows-1:
i = i + 1
else:
j = j + 1
if not has_symmetry:
i = 0
else:
i = j
if is_skew:
a[i, j] = 0
if i < rows-1:
i += 1
if is_skew:
if not (i in [0, j] and j == cols - 1):
raise ValueError("Parse error, did not read all lines.")
else:
if not (i in [0, j] and j == cols):
raise ValueError("Parse error, did not read all lines.")
elif format == self.FORMAT_COORDINATE and coo_matrix is None:
# Read sparse matrix to dense when coo_matrix is not available.
a = zeros((rows, cols), dtype=dtype)
line = 1
k = 0
while line:
line = stream.readline()
if not line or line.startswith(b'%'):
continue
l = line.split()
i, j = map(int, l[:2])
i, j = i-1, j-1
if is_integer:
aij = int(l[2])
elif is_unsigned_integer:
aij = int(l[2])
elif is_complex:
aij = complex(*map(float, l[2:]))
else:
aij = float(l[2])
a[i, j] = aij
if has_symmetry and i != j:
if is_skew:
a[j, i] = -aij
elif is_herm:
a[j, i] = conj(aij)
else:
a[j, i] = aij
k = k + 1
if not k == entries:
ValueError("Did not read all entries")
elif format == self.FORMAT_COORDINATE:
# Read sparse COOrdinate format
if entries == 0:
# empty matrix
return coo_matrix((rows, cols), dtype=dtype)
I = zeros(entries, dtype='intc')
J = zeros(entries, dtype='intc')
if is_pattern:
V = ones(entries, dtype='int8')
elif is_integer:
V = zeros(entries, dtype='intp')
elif is_unsigned_integer:
V = zeros(entries, dtype='uint64')
elif is_complex:
V = zeros(entries, dtype='complex')
else:
V = zeros(entries, dtype='float')
entry_number = 0
for line in stream:
if not line or line.startswith(b'%'):
continue
if entry_number+1 > entries:
raise ValueError("'entries' in header is smaller than "
"number of entries")
l = line.split()
I[entry_number], J[entry_number] = map(int, l[:2])
if not is_pattern:
if is_integer:
V[entry_number] = int(l[2])
elif is_unsigned_integer:
V[entry_number] = int(l[2])
elif is_complex:
V[entry_number] = complex(*map(float, l[2:]))
else:
V[entry_number] = float(l[2])
entry_number += 1
if entry_number < entries:
raise ValueError("'entries' in header is larger than "
"number of entries")
I -= 1 # adjust indices (base 1 -> base 0)
J -= 1
if has_symmetry:
mask = (I != J) # off diagonal mask
od_I = I[mask]
od_J = J[mask]
od_V = V[mask]
I = concatenate((I, od_J))
J = concatenate((J, od_I))
if is_skew:
od_V *= -1
elif is_herm:
od_V = od_V.conjugate()
V = concatenate((V, od_V))
a = coo_matrix((V, (I, J)), shape=(rows, cols), dtype=dtype)
else:
raise NotImplementedError(format)
return a
# ------------------------------------------------------------------------
def _write(self, stream, a, comment='', field=None, precision=None,
symmetry=None):
if isinstance(a, list) or isinstance(a, ndarray) or \
isinstance(a, tuple) or hasattr(a, '__array__'):
rep = self.FORMAT_ARRAY
a = asarray(a)
if len(a.shape) != 2:
raise ValueError('Expected 2 dimensional array')
rows, cols = a.shape
if field is not None:
if field == self.FIELD_INTEGER:
if not can_cast(a.dtype, 'intp'):
raise OverflowError("mmwrite does not support integer "
"dtypes larger than native 'intp'.")
a = a.astype('intp')
elif field == self.FIELD_REAL:
if a.dtype.char not in 'fd':
a = a.astype('d')
elif field == self.FIELD_COMPLEX:
if a.dtype.char not in 'FD':
a = a.astype('D')
else:
if not isspmatrix(a):
raise ValueError('unknown matrix type: %s' % type(a))
rep = 'coordinate'
rows, cols = a.shape
typecode = a.dtype.char
if precision is None:
if typecode in 'fF':
precision = 8
else:
precision = 16
if field is None:
kind = a.dtype.kind
if kind == 'i':
if not can_cast(a.dtype, 'intp'):
raise OverflowError("mmwrite does not support integer "
"dtypes larger than native 'intp'.")
field = 'integer'
elif kind == 'f':
field = 'real'
elif kind == 'c':
field = 'complex'
elif kind == 'u':
field = 'unsigned-integer'
else:
raise TypeError('unexpected dtype kind ' + kind)
if symmetry is None:
symmetry = self._get_symmetry(a)
# validate rep, field, and symmetry
self.__class__._validate_format(rep)
self.__class__._validate_field(field)
self.__class__._validate_symmetry(symmetry)
# write initial header line
stream.write(asbytes('%%MatrixMarket matrix {0} {1} {2}\n'.format(rep,
field, symmetry)))
# write comments
for line in comment.split('\n'):
stream.write(asbytes('%%%s\n' % (line)))
template = self._field_template(field, precision)
# write dense format
if rep == self.FORMAT_ARRAY:
# write shape spec
stream.write(asbytes('%i %i\n' % (rows, cols)))
if field in (self.FIELD_INTEGER, self.FIELD_REAL, self.FIELD_UNSIGNED):
if symmetry == self.SYMMETRY_GENERAL:
for j in range(cols):
for i in range(rows):
stream.write(asbytes(template % a[i, j]))
elif symmetry == self.SYMMETRY_SKEW_SYMMETRIC:
for j in range(cols):
for i in range(j + 1, rows):
stream.write(asbytes(template % a[i, j]))
else:
for j in range(cols):
for i in range(j, rows):
stream.write(asbytes(template % a[i, j]))
elif field == self.FIELD_COMPLEX:
if symmetry == self.SYMMETRY_GENERAL:
for j in range(cols):
for i in range(rows):
aij = a[i, j]
stream.write(asbytes(template % (real(aij),
imag(aij))))
else:
for j in range(cols):
for i in range(j, rows):
aij = a[i, j]
stream.write(asbytes(template % (real(aij),
imag(aij))))
elif field == self.FIELD_PATTERN:
raise ValueError('pattern type inconsisted with dense format')
else:
raise TypeError('Unknown field type %s' % field)
# write sparse format
else:
coo = a.tocoo() # convert to COOrdinate format
# if symmetry format used, remove values above main diagonal
if symmetry != self.SYMMETRY_GENERAL:
lower_triangle_mask = coo.row >= coo.col
coo = coo_matrix((coo.data[lower_triangle_mask],
(coo.row[lower_triangle_mask],
coo.col[lower_triangle_mask])),
shape=coo.shape)
# write shape spec
stream.write(asbytes('%i %i %i\n' % (rows, cols, coo.nnz)))
template = self._field_template(field, precision-1)
if field == self.FIELD_PATTERN:
for r, c in zip(coo.row+1, coo.col+1):
stream.write(asbytes("%i %i\n" % (r, c)))
elif field in (self.FIELD_INTEGER, self.FIELD_REAL, self.FIELD_UNSIGNED):
for r, c, d in zip(coo.row+1, coo.col+1, coo.data):
stream.write(asbytes(("%i %i " % (r, c)) +
(template % d)))
elif field == self.FIELD_COMPLEX:
for r, c, d in zip(coo.row+1, coo.col+1, coo.data):
stream.write(asbytes(("%i %i " % (r, c)) +
(template % (d.real, d.imag))))
else:
raise TypeError('Unknown field type %s' % field)
def _is_fromfile_compatible(stream):
"""
Check whether `stream` is compatible with numpy.fromfile.
Passing a gzipped file object to ``fromfile/fromstring`` doesn't work with
Python3.
"""
if sys.version_info[0] < 3:
return True
bad_cls = []
try:
import gzip
bad_cls.append(gzip.GzipFile)
except ImportError:
pass
try:
import bz2
bad_cls.append(bz2.BZ2File)
except ImportError:
pass
bad_cls = tuple(bad_cls)
return not isinstance(stream, bad_cls)
# -----------------------------------------------------------------------------
if __name__ == '__main__':
import time
for filename in sys.argv[1:]:
print('Reading', filename, '...', end=' ')
sys.stdout.flush()
t = time.time()
mmread(filename)
print('took %s seconds' % (time.time() - t))
| 28,897 | 33.525687 | 92 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/setup.py
|
from __future__ import division, print_function, absolute_import
def configuration(parent_package='',top_path=None):
from numpy.distutils.misc_util import Configuration
config = Configuration('io', parent_package, top_path)
config.add_extension('_test_fortran',
sources=['_test_fortran.pyf', '_test_fortran.f'])
config.add_data_dir('tests')
config.add_subpackage('matlab')
config.add_subpackage('arff')
config.add_subpackage('harwell_boeing')
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())
| 639 | 29.47619 | 74 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/netcdf.py
|
"""
NetCDF reader/writer module.
This module is used to read and create NetCDF files. NetCDF files are
accessed through the `netcdf_file` object. Data written to and from NetCDF
files are contained in `netcdf_variable` objects. Attributes are given
as member variables of the `netcdf_file` and `netcdf_variable` objects.
This module implements the Scientific.IO.NetCDF API to read and create
NetCDF files. The same API is also used in the PyNIO and pynetcdf
modules, allowing these modules to be used interchangeably when working
with NetCDF files.
Only NetCDF3 is supported here; for NetCDF4 see
`netCDF4-python <http://unidata.github.io/netcdf4-python/>`__,
which has a similar API.
"""
from __future__ import division, print_function, absolute_import
# TODO:
# * properly implement ``_FillValue``.
# * fix character variables.
# * implement PAGESIZE for Python 2.6?
# The Scientific.IO.NetCDF API allows attributes to be added directly to
# instances of ``netcdf_file`` and ``netcdf_variable``. To differentiate
# between user-set attributes and instance attributes, user-set attributes
# are automatically stored in the ``_attributes`` attribute by overloading
#``__setattr__``. This is the reason why the code sometimes uses
#``obj.__dict__['key'] = value``, instead of simply ``obj.key = value``;
# otherwise the key would be inserted into userspace attributes.
__all__ = ['netcdf_file']
import sys
import warnings
import weakref
from operator import mul
from collections import OrderedDict
import mmap as mm
import numpy as np
from numpy.compat import asbytes, asstr
from numpy import frombuffer, dtype, empty, array, asarray
from numpy import little_endian as LITTLE_ENDIAN
from functools import reduce
from scipy._lib.six import integer_types, text_type, binary_type
IS_PYPY = ('__pypy__' in sys.modules)
ABSENT = b'\x00\x00\x00\x00\x00\x00\x00\x00'
ZERO = b'\x00\x00\x00\x00'
NC_BYTE = b'\x00\x00\x00\x01'
NC_CHAR = b'\x00\x00\x00\x02'
NC_SHORT = b'\x00\x00\x00\x03'
NC_INT = b'\x00\x00\x00\x04'
NC_FLOAT = b'\x00\x00\x00\x05'
NC_DOUBLE = b'\x00\x00\x00\x06'
NC_DIMENSION = b'\x00\x00\x00\n'
NC_VARIABLE = b'\x00\x00\x00\x0b'
NC_ATTRIBUTE = b'\x00\x00\x00\x0c'
FILL_BYTE = b'\x81'
FILL_CHAR = b'\x00'
FILL_SHORT = b'\x80\x01'
FILL_INT = b'\x80\x00\x00\x01'
FILL_FLOAT = b'\x7C\xF0\x00\x00'
FILL_DOUBLE = b'\x47\x9E\x00\x00\x00\x00\x00\x00'
TYPEMAP = {NC_BYTE: ('b', 1),
NC_CHAR: ('c', 1),
NC_SHORT: ('h', 2),
NC_INT: ('i', 4),
NC_FLOAT: ('f', 4),
NC_DOUBLE: ('d', 8)}
FILLMAP = {NC_BYTE: FILL_BYTE,
NC_CHAR: FILL_CHAR,
NC_SHORT: FILL_SHORT,
NC_INT: FILL_INT,
NC_FLOAT: FILL_FLOAT,
NC_DOUBLE: FILL_DOUBLE}
REVERSE = {('b', 1): NC_BYTE,
('B', 1): NC_CHAR,
('c', 1): NC_CHAR,
('h', 2): NC_SHORT,
('i', 4): NC_INT,
('f', 4): NC_FLOAT,
('d', 8): NC_DOUBLE,
# these come from asarray(1).dtype.char and asarray('foo').dtype.char,
# used when getting the types from generic attributes.
('l', 4): NC_INT,
('S', 1): NC_CHAR}
class netcdf_file(object):
"""
A file object for NetCDF data.
A `netcdf_file` object has two standard attributes: `dimensions` and
`variables`. The values of both are dictionaries, mapping dimension
names to their associated lengths and variable names to variables,
respectively. Application programs should never modify these
dictionaries.
All other attributes correspond to global attributes defined in the
NetCDF file. Global file attributes are created by assigning to an
attribute of the `netcdf_file` object.
Parameters
----------
filename : string or file-like
string -> filename
mode : {'r', 'w', 'a'}, optional
read-write-append mode, default is 'r'
mmap : None or bool, optional
Whether to mmap `filename` when reading. Default is True
when `filename` is a file name, False when `filename` is a
file-like object. Note that when mmap is in use, data arrays
returned refer directly to the mmapped data on disk, and the
file cannot be closed as long as references to it exist.
version : {1, 2}, optional
version of netcdf to read / write, where 1 means *Classic
format* and 2 means *64-bit offset format*. Default is 1. See
`here <https://www.unidata.ucar.edu/software/netcdf/docs/netcdf_introduction.html#select_format>`__
for more info.
maskandscale : bool, optional
Whether to automatically scale and/or mask data based on attributes.
Default is False.
Notes
-----
The major advantage of this module over other modules is that it doesn't
require the code to be linked to the NetCDF libraries. This module is
derived from `pupynere <https://bitbucket.org/robertodealmeida/pupynere/>`_.
NetCDF files are a self-describing binary data format. The file contains
metadata that describes the dimensions and variables in the file. More
details about NetCDF files can be found `here
<https://www.unidata.ucar.edu/software/netcdf/docs/user_guide.html>`__. There
are three main sections to a NetCDF data structure:
1. Dimensions
2. Variables
3. Attributes
The dimensions section records the name and length of each dimension used
by the variables. The variables would then indicate which dimensions it
uses and any attributes such as data units, along with containing the data
values for the variable. It is good practice to include a
variable that is the same name as a dimension to provide the values for
that axes. Lastly, the attributes section would contain additional
information such as the name of the file creator or the instrument used to
collect the data.
When writing data to a NetCDF file, there is often the need to indicate the
'record dimension'. A record dimension is the unbounded dimension for a
variable. For example, a temperature variable may have dimensions of
latitude, longitude and time. If one wants to add more temperature data to
the NetCDF file as time progresses, then the temperature variable should
have the time dimension flagged as the record dimension.
In addition, the NetCDF file header contains the position of the data in
the file, so access can be done in an efficient manner without loading
unnecessary data into memory. It uses the ``mmap`` module to create
Numpy arrays mapped to the data on disk, for the same purpose.
Note that when `netcdf_file` is used to open a file with mmap=True
(default for read-only), arrays returned by it refer to data
directly on the disk. The file should not be closed, and cannot be cleanly
closed when asked, if such arrays are alive. You may want to copy data arrays
obtained from mmapped Netcdf file if they are to be processed after the file
is closed, see the example below.
Examples
--------
To create a NetCDF file:
>>> from scipy.io import netcdf
>>> f = netcdf.netcdf_file('simple.nc', 'w')
>>> f.history = 'Created for a test'
>>> f.createDimension('time', 10)
>>> time = f.createVariable('time', 'i', ('time',))
>>> time[:] = np.arange(10)
>>> time.units = 'days since 2008-01-01'
>>> f.close()
Note the assignment of ``arange(10)`` to ``time[:]``. Exposing the slice
of the time variable allows for the data to be set in the object, rather
than letting ``arange(10)`` overwrite the ``time`` variable.
To read the NetCDF file we just created:
>>> from scipy.io import netcdf
>>> f = netcdf.netcdf_file('simple.nc', 'r')
>>> print(f.history)
b'Created for a test'
>>> time = f.variables['time']
>>> print(time.units)
b'days since 2008-01-01'
>>> print(time.shape)
(10,)
>>> print(time[-1])
9
NetCDF files, when opened read-only, return arrays that refer
directly to memory-mapped data on disk:
>>> data = time[:]
>>> data.base.base
<mmap.mmap object at 0x7fe753763180>
If the data is to be processed after the file is closed, it needs
to be copied to main memory:
>>> data = time[:].copy()
>>> f.close()
>>> data.mean()
4.5
A NetCDF file can also be used as context manager:
>>> from scipy.io import netcdf
>>> with netcdf.netcdf_file('simple.nc', 'r') as f:
... print(f.history)
b'Created for a test'
"""
def __init__(self, filename, mode='r', mmap=None, version=1,
maskandscale=False):
"""Initialize netcdf_file from fileobj (str or file-like)."""
if mode not in 'rwa':
raise ValueError("Mode must be either 'r', 'w' or 'a'.")
if hasattr(filename, 'seek'): # file-like
self.fp = filename
self.filename = 'None'
if mmap is None:
mmap = False
elif mmap and not hasattr(filename, 'fileno'):
raise ValueError('Cannot use file object for mmap')
else: # maybe it's a string
self.filename = filename
omode = 'r+' if mode == 'a' else mode
self.fp = open(self.filename, '%sb' % omode)
if mmap is None:
# Mmapped files on PyPy cannot be usually closed
# before the GC runs, so it's better to use mmap=False
# as the default.
mmap = (not IS_PYPY)
if mode != 'r':
# Cannot read write-only files
mmap = False
self.use_mmap = mmap
self.mode = mode
self.version_byte = version
self.maskandscale = maskandscale
self.dimensions = OrderedDict()
self.variables = OrderedDict()
self._dims = []
self._recs = 0
self._recsize = 0
self._mm = None
self._mm_buf = None
if self.use_mmap:
self._mm = mm.mmap(self.fp.fileno(), 0, access=mm.ACCESS_READ)
self._mm_buf = np.frombuffer(self._mm, dtype=np.int8)
self._attributes = OrderedDict()
if mode in 'ra':
self._read()
def __setattr__(self, attr, value):
# Store user defined attributes in a separate dict,
# so we can save them to file later.
try:
self._attributes[attr] = value
except AttributeError:
pass
self.__dict__[attr] = value
def close(self):
"""Closes the NetCDF file."""
if hasattr(self, 'fp') and not self.fp.closed:
try:
self.flush()
finally:
self.variables = OrderedDict()
if self._mm_buf is not None:
ref = weakref.ref(self._mm_buf)
self._mm_buf = None
if ref() is None:
# self._mm_buf is gc'd, and we can close the mmap
self._mm.close()
else:
# we cannot close self._mm, since self._mm_buf is
# alive and there may still be arrays referring to it
warnings.warn((
"Cannot close a netcdf_file opened with mmap=True, when "
"netcdf_variables or arrays referring to its data still exist. "
"All data arrays obtained from such files refer directly to "
"data on disk, and must be copied before the file can be cleanly "
"closed. (See netcdf_file docstring for more information on mmap.)"
), category=RuntimeWarning)
self._mm = None
self.fp.close()
__del__ = close
def __enter__(self):
return self
def __exit__(self, type, value, traceback):
self.close()
def createDimension(self, name, length):
"""
Adds a dimension to the Dimension section of the NetCDF data structure.
Note that this function merely adds a new dimension that the variables can
reference. The values for the dimension, if desired, should be added as
a variable using `createVariable`, referring to this dimension.
Parameters
----------
name : str
Name of the dimension (Eg, 'lat' or 'time').
length : int
Length of the dimension.
See Also
--------
createVariable
"""
if length is None and self._dims:
raise ValueError("Only first dimension may be unlimited!")
self.dimensions[name] = length
self._dims.append(name)
def createVariable(self, name, type, dimensions):
"""
Create an empty variable for the `netcdf_file` object, specifying its data
type and the dimensions it uses.
Parameters
----------
name : str
Name of the new variable.
type : dtype or str
Data type of the variable.
dimensions : sequence of str
List of the dimension names used by the variable, in the desired order.
Returns
-------
variable : netcdf_variable
The newly created ``netcdf_variable`` object.
This object has also been added to the `netcdf_file` object as well.
See Also
--------
createDimension
Notes
-----
Any dimensions to be used by the variable should already exist in the
NetCDF data structure or should be created by `createDimension` prior to
creating the NetCDF variable.
"""
shape = tuple([self.dimensions[dim] for dim in dimensions])
shape_ = tuple([dim or 0 for dim in shape]) # replace None with 0 for numpy
type = dtype(type)
typecode, size = type.char, type.itemsize
if (typecode, size) not in REVERSE:
raise ValueError("NetCDF 3 does not support type %s" % type)
data = empty(shape_, dtype=type.newbyteorder("B")) # convert to big endian always for NetCDF 3
self.variables[name] = netcdf_variable(
data, typecode, size, shape, dimensions,
maskandscale=self.maskandscale)
return self.variables[name]
def flush(self):
"""
Perform a sync-to-disk flush if the `netcdf_file` object is in write mode.
See Also
--------
sync : Identical function
"""
if hasattr(self, 'mode') and self.mode in 'wa':
self._write()
sync = flush
def _write(self):
self.fp.seek(0)
self.fp.write(b'CDF')
self.fp.write(array(self.version_byte, '>b').tostring())
# Write headers and data.
self._write_numrecs()
self._write_dim_array()
self._write_gatt_array()
self._write_var_array()
def _write_numrecs(self):
# Get highest record count from all record variables.
for var in self.variables.values():
if var.isrec and len(var.data) > self._recs:
self.__dict__['_recs'] = len(var.data)
self._pack_int(self._recs)
def _write_dim_array(self):
if self.dimensions:
self.fp.write(NC_DIMENSION)
self._pack_int(len(self.dimensions))
for name in self._dims:
self._pack_string(name)
length = self.dimensions[name]
self._pack_int(length or 0) # replace None with 0 for record dimension
else:
self.fp.write(ABSENT)
def _write_gatt_array(self):
self._write_att_array(self._attributes)
def _write_att_array(self, attributes):
if attributes:
self.fp.write(NC_ATTRIBUTE)
self._pack_int(len(attributes))
for name, values in attributes.items():
self._pack_string(name)
self._write_att_values(values)
else:
self.fp.write(ABSENT)
def _write_var_array(self):
if self.variables:
self.fp.write(NC_VARIABLE)
self._pack_int(len(self.variables))
# Sort variable names non-recs first, then recs.
def sortkey(n):
v = self.variables[n]
if v.isrec:
return (-1,)
return v._shape
variables = sorted(self.variables, key=sortkey, reverse=True)
# Set the metadata for all variables.
for name in variables:
self._write_var_metadata(name)
# Now that we have the metadata, we know the vsize of
# each record variable, so we can calculate recsize.
self.__dict__['_recsize'] = sum([
var._vsize for var in self.variables.values()
if var.isrec])
# Set the data for all variables.
for name in variables:
self._write_var_data(name)
else:
self.fp.write(ABSENT)
def _write_var_metadata(self, name):
var = self.variables[name]
self._pack_string(name)
self._pack_int(len(var.dimensions))
for dimname in var.dimensions:
dimid = self._dims.index(dimname)
self._pack_int(dimid)
self._write_att_array(var._attributes)
nc_type = REVERSE[var.typecode(), var.itemsize()]
self.fp.write(asbytes(nc_type))
if not var.isrec:
vsize = var.data.size * var.data.itemsize
vsize += -vsize % 4
else: # record variable
try:
vsize = var.data[0].size * var.data.itemsize
except IndexError:
vsize = 0
rec_vars = len([v for v in self.variables.values()
if v.isrec])
if rec_vars > 1:
vsize += -vsize % 4
self.variables[name].__dict__['_vsize'] = vsize
self._pack_int(vsize)
# Pack a bogus begin, and set the real value later.
self.variables[name].__dict__['_begin'] = self.fp.tell()
self._pack_begin(0)
def _write_var_data(self, name):
var = self.variables[name]
# Set begin in file header.
the_beguine = self.fp.tell()
self.fp.seek(var._begin)
self._pack_begin(the_beguine)
self.fp.seek(the_beguine)
# Write data.
if not var.isrec:
self.fp.write(var.data.tostring())
count = var.data.size * var.data.itemsize
self._write_var_padding(var, var._vsize - count)
else: # record variable
# Handle rec vars with shape[0] < nrecs.
if self._recs > len(var.data):
shape = (self._recs,) + var.data.shape[1:]
# Resize in-place does not always work since
# the array might not be single-segment
try:
var.data.resize(shape)
except ValueError:
var.__dict__['data'] = np.resize(var.data, shape).astype(var.data.dtype)
pos0 = pos = self.fp.tell()
for rec in var.data:
# Apparently scalars cannot be converted to big endian. If we
# try to convert a ``=i4`` scalar to, say, '>i4' the dtype
# will remain as ``=i4``.
if not rec.shape and (rec.dtype.byteorder == '<' or
(rec.dtype.byteorder == '=' and LITTLE_ENDIAN)):
rec = rec.byteswap()
self.fp.write(rec.tostring())
# Padding
count = rec.size * rec.itemsize
self._write_var_padding(var, var._vsize - count)
pos += self._recsize
self.fp.seek(pos)
self.fp.seek(pos0 + var._vsize)
def _write_var_padding(self, var, size):
encoded_fill_value = var._get_encoded_fill_value()
num_fills = size // len(encoded_fill_value)
self.fp.write(encoded_fill_value * num_fills)
def _write_att_values(self, values):
if hasattr(values, 'dtype'):
nc_type = REVERSE[values.dtype.char, values.dtype.itemsize]
else:
types = [(t, NC_INT) for t in integer_types]
types += [
(float, NC_FLOAT),
(str, NC_CHAR)
]
# bytes index into scalars in py3k. Check for "string" types
if isinstance(values, text_type) or isinstance(values, binary_type):
sample = values
else:
try:
sample = values[0] # subscriptable?
except TypeError:
sample = values # scalar
for class_, nc_type in types:
if isinstance(sample, class_):
break
typecode, size = TYPEMAP[nc_type]
dtype_ = '>%s' % typecode
# asarray() dies with bytes and '>c' in py3k. Change to 'S'
dtype_ = 'S' if dtype_ == '>c' else dtype_
values = asarray(values, dtype=dtype_)
self.fp.write(asbytes(nc_type))
if values.dtype.char == 'S':
nelems = values.itemsize
else:
nelems = values.size
self._pack_int(nelems)
if not values.shape and (values.dtype.byteorder == '<' or
(values.dtype.byteorder == '=' and LITTLE_ENDIAN)):
values = values.byteswap()
self.fp.write(values.tostring())
count = values.size * values.itemsize
self.fp.write(b'\x00' * (-count % 4)) # pad
def _read(self):
# Check magic bytes and version
magic = self.fp.read(3)
if not magic == b'CDF':
raise TypeError("Error: %s is not a valid NetCDF 3 file" %
self.filename)
self.__dict__['version_byte'] = frombuffer(self.fp.read(1), '>b')[0]
# Read file headers and set data.
self._read_numrecs()
self._read_dim_array()
self._read_gatt_array()
self._read_var_array()
def _read_numrecs(self):
self.__dict__['_recs'] = self._unpack_int()
def _read_dim_array(self):
header = self.fp.read(4)
if header not in [ZERO, NC_DIMENSION]:
raise ValueError("Unexpected header.")
count = self._unpack_int()
for dim in range(count):
name = asstr(self._unpack_string())
length = self._unpack_int() or None # None for record dimension
self.dimensions[name] = length
self._dims.append(name) # preserve order
def _read_gatt_array(self):
for k, v in self._read_att_array().items():
self.__setattr__(k, v)
def _read_att_array(self):
header = self.fp.read(4)
if header not in [ZERO, NC_ATTRIBUTE]:
raise ValueError("Unexpected header.")
count = self._unpack_int()
attributes = OrderedDict()
for attr in range(count):
name = asstr(self._unpack_string())
attributes[name] = self._read_att_values()
return attributes
def _read_var_array(self):
header = self.fp.read(4)
if header not in [ZERO, NC_VARIABLE]:
raise ValueError("Unexpected header.")
begin = 0
dtypes = {'names': [], 'formats': []}
rec_vars = []
count = self._unpack_int()
for var in range(count):
(name, dimensions, shape, attributes,
typecode, size, dtype_, begin_, vsize) = self._read_var()
# https://www.unidata.ucar.edu/software/netcdf/docs/user_guide.html
# Note that vsize is the product of the dimension lengths
# (omitting the record dimension) and the number of bytes
# per value (determined from the type), increased to the
# next multiple of 4, for each variable. If a record
# variable, this is the amount of space per record. The
# netCDF "record size" is calculated as the sum of the
# vsize's of all the record variables.
#
# The vsize field is actually redundant, because its value
# may be computed from other information in the header. The
# 32-bit vsize field is not large enough to contain the size
# of variables that require more than 2^32 - 4 bytes, so
# 2^32 - 1 is used in the vsize field for such variables.
if shape and shape[0] is None: # record variable
rec_vars.append(name)
# The netCDF "record size" is calculated as the sum of
# the vsize's of all the record variables.
self.__dict__['_recsize'] += vsize
if begin == 0:
begin = begin_
dtypes['names'].append(name)
dtypes['formats'].append(str(shape[1:]) + dtype_)
# Handle padding with a virtual variable.
if typecode in 'bch':
actual_size = reduce(mul, (1,) + shape[1:]) * size
padding = -actual_size % 4
if padding:
dtypes['names'].append('_padding_%d' % var)
dtypes['formats'].append('(%d,)>b' % padding)
# Data will be set later.
data = None
else: # not a record variable
# Calculate size to avoid problems with vsize (above)
a_size = reduce(mul, shape, 1) * size
if self.use_mmap:
data = self._mm_buf[begin_:begin_+a_size].view(dtype=dtype_)
data.shape = shape
else:
pos = self.fp.tell()
self.fp.seek(begin_)
data = frombuffer(self.fp.read(a_size), dtype=dtype_
).copy()
data.shape = shape
self.fp.seek(pos)
# Add variable.
self.variables[name] = netcdf_variable(
data, typecode, size, shape, dimensions, attributes,
maskandscale=self.maskandscale)
if rec_vars:
# Remove padding when only one record variable.
if len(rec_vars) == 1:
dtypes['names'] = dtypes['names'][:1]
dtypes['formats'] = dtypes['formats'][:1]
# Build rec array.
if self.use_mmap:
rec_array = self._mm_buf[begin:begin+self._recs*self._recsize].view(dtype=dtypes)
rec_array.shape = (self._recs,)
else:
pos = self.fp.tell()
self.fp.seek(begin)
rec_array = frombuffer(self.fp.read(self._recs*self._recsize),
dtype=dtypes).copy()
rec_array.shape = (self._recs,)
self.fp.seek(pos)
for var in rec_vars:
self.variables[var].__dict__['data'] = rec_array[var]
def _read_var(self):
name = asstr(self._unpack_string())
dimensions = []
shape = []
dims = self._unpack_int()
for i in range(dims):
dimid = self._unpack_int()
dimname = self._dims[dimid]
dimensions.append(dimname)
dim = self.dimensions[dimname]
shape.append(dim)
dimensions = tuple(dimensions)
shape = tuple(shape)
attributes = self._read_att_array()
nc_type = self.fp.read(4)
vsize = self._unpack_int()
begin = [self._unpack_int, self._unpack_int64][self.version_byte-1]()
typecode, size = TYPEMAP[nc_type]
dtype_ = '>%s' % typecode
return name, dimensions, shape, attributes, typecode, size, dtype_, begin, vsize
def _read_att_values(self):
nc_type = self.fp.read(4)
n = self._unpack_int()
typecode, size = TYPEMAP[nc_type]
count = n*size
values = self.fp.read(int(count))
self.fp.read(-count % 4) # read padding
if typecode is not 'c':
values = frombuffer(values, dtype='>%s' % typecode).copy()
if values.shape == (1,):
values = values[0]
else:
values = values.rstrip(b'\x00')
return values
def _pack_begin(self, begin):
if self.version_byte == 1:
self._pack_int(begin)
elif self.version_byte == 2:
self._pack_int64(begin)
def _pack_int(self, value):
self.fp.write(array(value, '>i').tostring())
_pack_int32 = _pack_int
def _unpack_int(self):
return int(frombuffer(self.fp.read(4), '>i')[0])
_unpack_int32 = _unpack_int
def _pack_int64(self, value):
self.fp.write(array(value, '>q').tostring())
def _unpack_int64(self):
return frombuffer(self.fp.read(8), '>q')[0]
def _pack_string(self, s):
count = len(s)
self._pack_int(count)
self.fp.write(asbytes(s))
self.fp.write(b'\x00' * (-count % 4)) # pad
def _unpack_string(self):
count = self._unpack_int()
s = self.fp.read(count).rstrip(b'\x00')
self.fp.read(-count % 4) # read padding
return s
class netcdf_variable(object):
"""
A data object for the `netcdf` module.
`netcdf_variable` objects are constructed by calling the method
`netcdf_file.createVariable` on the `netcdf_file` object. `netcdf_variable`
objects behave much like array objects defined in numpy, except that their
data resides in a file. Data is read by indexing and written by assigning
to an indexed subset; the entire array can be accessed by the index ``[:]``
or (for scalars) by using the methods `getValue` and `assignValue`.
`netcdf_variable` objects also have attribute `shape` with the same meaning
as for arrays, but the shape cannot be modified. There is another read-only
attribute `dimensions`, whose value is the tuple of dimension names.
All other attributes correspond to variable attributes defined in
the NetCDF file. Variable attributes are created by assigning to an
attribute of the `netcdf_variable` object.
Parameters
----------
data : array_like
The data array that holds the values for the variable.
Typically, this is initialized as empty, but with the proper shape.
typecode : dtype character code
Desired data-type for the data array.
size : int
Desired element size for the data array.
shape : sequence of ints
The shape of the array. This should match the lengths of the
variable's dimensions.
dimensions : sequence of strings
The names of the dimensions used by the variable. Must be in the
same order of the dimension lengths given by `shape`.
attributes : dict, optional
Attribute values (any type) keyed by string names. These attributes
become attributes for the netcdf_variable object.
maskandscale : bool, optional
Whether to automatically scale and/or mask data based on attributes.
Default is False.
Attributes
----------
dimensions : list of str
List of names of dimensions used by the variable object.
isrec, shape
Properties
See also
--------
isrec, shape
"""
def __init__(self, data, typecode, size, shape, dimensions,
attributes=None,
maskandscale=False):
self.data = data
self._typecode = typecode
self._size = size
self._shape = shape
self.dimensions = dimensions
self.maskandscale = maskandscale
self._attributes = attributes or OrderedDict()
for k, v in self._attributes.items():
self.__dict__[k] = v
def __setattr__(self, attr, value):
# Store user defined attributes in a separate dict,
# so we can save them to file later.
try:
self._attributes[attr] = value
except AttributeError:
pass
self.__dict__[attr] = value
def isrec(self):
"""Returns whether the variable has a record dimension or not.
A record dimension is a dimension along which additional data could be
easily appended in the netcdf data structure without much rewriting of
the data file. This attribute is a read-only property of the
`netcdf_variable`.
"""
return bool(self.data.shape) and not self._shape[0]
isrec = property(isrec)
def shape(self):
"""Returns the shape tuple of the data variable.
This is a read-only attribute and can not be modified in the
same manner of other numpy arrays.
"""
return self.data.shape
shape = property(shape)
def getValue(self):
"""
Retrieve a scalar value from a `netcdf_variable` of length one.
Raises
------
ValueError
If the netcdf variable is an array of length greater than one,
this exception will be raised.
"""
return self.data.item()
def assignValue(self, value):
"""
Assign a scalar value to a `netcdf_variable` of length one.
Parameters
----------
value : scalar
Scalar value (of compatible type) to assign to a length-one netcdf
variable. This value will be written to file.
Raises
------
ValueError
If the input is not a scalar, or if the destination is not a length-one
netcdf variable.
"""
if not self.data.flags.writeable:
# Work-around for a bug in NumPy. Calling itemset() on a read-only
# memory-mapped array causes a seg. fault.
# See NumPy ticket #1622, and SciPy ticket #1202.
# This check for `writeable` can be removed when the oldest version
# of numpy still supported by scipy contains the fix for #1622.
raise RuntimeError("variable is not writeable")
self.data.itemset(value)
def typecode(self):
"""
Return the typecode of the variable.
Returns
-------
typecode : char
The character typecode of the variable (eg, 'i' for int).
"""
return self._typecode
def itemsize(self):
"""
Return the itemsize of the variable.
Returns
-------
itemsize : int
The element size of the variable (eg, 8 for float64).
"""
return self._size
def __getitem__(self, index):
if not self.maskandscale:
return self.data[index]
data = self.data[index].copy()
missing_value = self._get_missing_value()
data = self._apply_missing_value(data, missing_value)
scale_factor = self._attributes.get('scale_factor')
add_offset = self._attributes.get('add_offset')
if add_offset is not None or scale_factor is not None:
data = data.astype(np.float64)
if scale_factor is not None:
data = data * scale_factor
if add_offset is not None:
data += add_offset
return data
def __setitem__(self, index, data):
if self.maskandscale:
missing_value = (
self._get_missing_value() or
getattr(data, 'fill_value', 999999))
self._attributes.setdefault('missing_value', missing_value)
self._attributes.setdefault('_FillValue', missing_value)
data = ((data - self._attributes.get('add_offset', 0.0)) /
self._attributes.get('scale_factor', 1.0))
data = np.ma.asarray(data).filled(missing_value)
if self._typecode not in 'fd' and data.dtype.kind == 'f':
data = np.round(data)
# Expand data for record vars?
if self.isrec:
if isinstance(index, tuple):
rec_index = index[0]
else:
rec_index = index
if isinstance(rec_index, slice):
recs = (rec_index.start or 0) + len(data)
else:
recs = rec_index + 1
if recs > len(self.data):
shape = (recs,) + self._shape[1:]
# Resize in-place does not always work since
# the array might not be single-segment
try:
self.data.resize(shape)
except ValueError:
self.__dict__['data'] = np.resize(self.data, shape).astype(self.data.dtype)
self.data[index] = data
def _default_encoded_fill_value(self):
"""
The default encoded fill-value for this Variable's data type.
"""
nc_type = REVERSE[self.typecode(), self.itemsize()]
return FILLMAP[nc_type]
def _get_encoded_fill_value(self):
"""
Returns the encoded fill value for this variable as bytes.
This is taken from either the _FillValue attribute, or the default fill
value for this variable's data type.
"""
if '_FillValue' in self._attributes:
fill_value = np.array(self._attributes['_FillValue'],
dtype=self.data.dtype).tostring()
if len(fill_value) == self.itemsize():
return fill_value
else:
return self._default_encoded_fill_value()
else:
return self._default_encoded_fill_value()
def _get_missing_value(self):
"""
Returns the value denoting "no data" for this variable.
If this variable does not have a missing/fill value, returns None.
If both _FillValue and missing_value are given, give precedence to
_FillValue. The netCDF standard gives special meaning to _FillValue;
missing_value is just used for compatibility with old datasets.
"""
if '_FillValue' in self._attributes:
missing_value = self._attributes['_FillValue']
elif 'missing_value' in self._attributes:
missing_value = self._attributes['missing_value']
else:
missing_value = None
return missing_value
@staticmethod
def _apply_missing_value(data, missing_value):
"""
Applies the given missing value to the data array.
Returns a numpy.ma array, with any value equal to missing_value masked
out (unless missing_value is None, in which case the original array is
returned).
"""
if missing_value is None:
newdata = data
else:
try:
missing_value_isnan = np.isnan(missing_value)
except (TypeError, NotImplementedError):
# some data types (e.g., characters) cannot be tested for NaN
missing_value_isnan = False
if missing_value_isnan:
mymask = np.isnan(data)
else:
mymask = (data == missing_value)
newdata = np.ma.masked_where(mymask, data)
return newdata
NetCDFFile = netcdf_file
NetCDFVariable = netcdf_variable
| 39,509 | 34.950864 | 107 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/_fortran.py
|
"""
Module to read / write Fortran unformatted sequential files.
This is in the spirit of code written by Neil Martinsen-Burrell and Joe Zuntz.
"""
from __future__ import division, print_function, absolute_import
import warnings
import numpy as np
__all__ = ['FortranFile']
class FortranFile(object):
"""
A file object for unformatted sequential files from Fortran code.
Parameters
----------
filename : file or str
Open file object or filename.
mode : {'r', 'w'}, optional
Read-write mode, default is 'r'.
header_dtype : dtype, optional
Data type of the header. Size and endiness must match the input/output file.
Notes
-----
These files are broken up into records of unspecified types. The size of
each record is given at the start (although the size of this header is not
standard) and the data is written onto disk without any formatting. Fortran
compilers supporting the BACKSPACE statement will write a second copy of
the size to facilitate backwards seeking.
This class only supports files written with both sizes for the record.
It also does not support the subrecords used in Intel and gfortran compilers
for records which are greater than 2GB with a 4-byte header.
An example of an unformatted sequential file in Fortran would be written as::
OPEN(1, FILE=myfilename, FORM='unformatted')
WRITE(1) myvariable
Since this is a non-standard file format, whose contents depend on the
compiler and the endianness of the machine, caution is advised. Files from
gfortran 4.8.0 and gfortran 4.1.2 on x86_64 are known to work.
Consider using Fortran direct-access files or files from the newer Stream
I/O, which can be easily read by `numpy.fromfile`.
Examples
--------
To create an unformatted sequential Fortran file:
>>> from scipy.io import FortranFile
>>> f = FortranFile('test.unf', 'w')
>>> f.write_record(np.array([1,2,3,4,5], dtype=np.int32))
>>> f.write_record(np.linspace(0,1,20).reshape((5,4)).T)
>>> f.close()
To read this file:
>>> f = FortranFile('test.unf', 'r')
>>> print(f.read_ints(np.int32))
[1 2 3 4 5]
>>> print(f.read_reals(float).reshape((5,4), order="F"))
[[0. 0.05263158 0.10526316 0.15789474]
[0.21052632 0.26315789 0.31578947 0.36842105]
[0.42105263 0.47368421 0.52631579 0.57894737]
[0.63157895 0.68421053 0.73684211 0.78947368]
[0.84210526 0.89473684 0.94736842 1. ]]
>>> f.close()
Or, in Fortran::
integer :: a(5), i
double precision :: b(5,4)
open(1, file='test.unf', form='unformatted')
read(1) a
read(1) b
close(1)
write(*,*) a
do i = 1, 5
write(*,*) b(i,:)
end do
"""
def __init__(self, filename, mode='r', header_dtype=np.uint32):
if header_dtype is None:
raise ValueError('Must specify dtype')
header_dtype = np.dtype(header_dtype)
if header_dtype.kind != 'u':
warnings.warn("Given a dtype which is not unsigned.")
if mode not in 'rw' or len(mode) != 1:
raise ValueError('mode must be either r or w')
if hasattr(filename, 'seek'):
self._fp = filename
else:
self._fp = open(filename, '%sb' % mode)
self._header_dtype = header_dtype
def _read_size(self):
return int(np.fromfile(self._fp, dtype=self._header_dtype, count=1))
def write_record(self, *items):
"""
Write a record (including sizes) to the file.
Parameters
----------
*items : array_like
The data arrays to write.
Notes
-----
Writes data items to a file::
write_record(a.T, b.T, c.T, ...)
write(1) a, b, c, ...
Note that data in multidimensional arrays is written in
row-major order --- to make them read correctly by Fortran
programs, you need to transpose the arrays yourself when
writing them.
"""
items = tuple(np.asarray(item) for item in items)
total_size = sum(item.nbytes for item in items)
nb = np.array([total_size], dtype=self._header_dtype)
nb.tofile(self._fp)
for item in items:
item.tofile(self._fp)
nb.tofile(self._fp)
def read_record(self, *dtypes, **kwargs):
"""
Reads a record of a given type from the file.
Parameters
----------
*dtypes : dtypes, optional
Data type(s) specifying the size and endiness of the data.
Returns
-------
data : ndarray
A one-dimensional array object.
Notes
-----
If the record contains a multi-dimensional array, you can specify
the size in the dtype. For example::
INTEGER var(5,4)
can be read with::
read_record('(4,5)i4').T
Note that this function does **not** assume the file data is in Fortran
column major order, so you need to (i) swap the order of dimensions
when reading and (ii) transpose the resulting array.
Alternatively, you can read the data as a 1D array and handle the
ordering yourself. For example::
read_record('i4').reshape(5, 4, order='F')
For records that contain several variables or mixed types (as opposed
to single scalar or array types), give them as separate arguments::
double precision :: a
integer :: b
write(1) a, b
record = f.read_record('<f4', '<i4')
a = record[0] # first number
b = record[1] # second number
and if any of the variables are arrays, the shape can be specified as
the third item in the relevant dtype::
double precision :: a
integer :: b(3,4)
write(1) a, b
record = f.read_record('<f4', np.dtype(('<i4', (4, 3))))
a = record[0]
b = record[1].T
Numpy also supports a short syntax for this kind of type::
record = f.read_record('<f4', '(3,3)<i4')
See Also
--------
read_reals
read_ints
"""
dtype = kwargs.pop('dtype', None)
if kwargs:
raise ValueError("Unknown keyword arguments {}".format(tuple(kwargs.keys())))
if dtype is not None:
dtypes = dtypes + (dtype,)
elif not dtypes:
raise ValueError('Must specify at least one dtype')
first_size = self._read_size()
dtypes = tuple(np.dtype(dtype) for dtype in dtypes)
block_size = sum(dtype.itemsize for dtype in dtypes)
num_blocks, remainder = divmod(first_size, block_size)
if remainder != 0:
raise ValueError('Size obtained ({0}) is not a multiple of the '
'dtypes given ({1}).'.format(first_size, block_size))
if len(dtypes) != 1 and first_size != block_size:
# Fortran does not write mixed type array items in interleaved order,
# and it's not possible to guess the sizes of the arrays that were written.
# The user must specify the exact sizes of each of the arrays.
raise ValueError('Size obtained ({0}) does not match with the expected '
'size ({1}) of multi-item record'.format(first_size, block_size))
data = []
for dtype in dtypes:
r = np.fromfile(self._fp, dtype=dtype, count=num_blocks)
if dtype.shape != ():
# Squeeze outmost block dimension for array items
if num_blocks == 1:
assert r.shape == (1,) + dtype.shape
r = r[0]
data.append(r)
second_size = self._read_size()
if first_size != second_size:
raise IOError('Sizes do not agree in the header and footer for '
'this record - check header dtype')
# Unpack result
if len(dtypes) == 1:
return data[0]
else:
return tuple(data)
def read_ints(self, dtype='i4'):
"""
Reads a record of a given type from the file, defaulting to an integer
type (``INTEGER*4`` in Fortran).
Parameters
----------
dtype : dtype, optional
Data type specifying the size and endiness of the data.
Returns
-------
data : ndarray
A one-dimensional array object.
See Also
--------
read_reals
read_record
"""
return self.read_record(dtype)
def read_reals(self, dtype='f8'):
"""
Reads a record of a given type from the file, defaulting to a floating
point number (``real*8`` in Fortran).
Parameters
----------
dtype : dtype, optional
Data type specifying the size and endiness of the data.
Returns
-------
data : ndarray
A one-dimensional array object.
See Also
--------
read_ints
read_record
"""
return self.read_record(dtype)
def close(self):
"""
Closes the file. It is unsupported to call any other methods off this
object after closing it. Note that this class supports the 'with'
statement in modern versions of Python, to call this automatically
"""
self._fp.close()
def __enter__(self):
return self
def __exit__(self, type, value, tb):
self.close()
| 9,737 | 29.622642 | 94 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/wavfile.py
|
"""
Module to read / write wav files using numpy arrays
Functions
---------
`read`: Return the sample rate (in samples/sec) and data from a WAV file.
`write`: Write a numpy array as a WAV file.
"""
from __future__ import division, print_function, absolute_import
import sys
import numpy
import struct
import warnings
__all__ = [
'WavFileWarning',
'read',
'write'
]
class WavFileWarning(UserWarning):
pass
WAVE_FORMAT_PCM = 0x0001
WAVE_FORMAT_IEEE_FLOAT = 0x0003
WAVE_FORMAT_EXTENSIBLE = 0xfffe
KNOWN_WAVE_FORMATS = (WAVE_FORMAT_PCM, WAVE_FORMAT_IEEE_FLOAT)
# assumes file pointer is immediately
# after the 'fmt ' id
def _read_fmt_chunk(fid, is_big_endian):
"""
Returns
-------
size : int
size of format subchunk in bytes (minus 8 for "fmt " and itself)
format_tag : int
PCM, float, or compressed format
channels : int
number of channels
fs : int
sampling frequency in samples per second
bytes_per_second : int
overall byte rate for the file
block_align : int
bytes per sample, including all channels
bit_depth : int
bits per sample
"""
if is_big_endian:
fmt = '>'
else:
fmt = '<'
size = res = struct.unpack(fmt+'I', fid.read(4))[0]
bytes_read = 0
if size < 16:
raise ValueError("Binary structure of wave file is not compliant")
res = struct.unpack(fmt+'HHIIHH', fid.read(16))
bytes_read += 16
format_tag, channels, fs, bytes_per_second, block_align, bit_depth = res
if format_tag == WAVE_FORMAT_EXTENSIBLE and size >= (16+2):
ext_chunk_size = struct.unpack(fmt+'H', fid.read(2))[0]
bytes_read += 2
if ext_chunk_size >= 22:
extensible_chunk_data = fid.read(22)
bytes_read += 22
raw_guid = extensible_chunk_data[2+4:2+4+16]
# GUID template {XXXXXXXX-0000-0010-8000-00AA00389B71} (RFC-2361)
# MS GUID byte order: first three groups are native byte order,
# rest is Big Endian
if is_big_endian:
tail = b'\x00\x00\x00\x10\x80\x00\x00\xAA\x00\x38\x9B\x71'
else:
tail = b'\x00\x00\x10\x00\x80\x00\x00\xAA\x00\x38\x9B\x71'
if raw_guid.endswith(tail):
format_tag = struct.unpack(fmt+'I', raw_guid[:4])[0]
else:
raise ValueError("Binary structure of wave file is not compliant")
if format_tag not in KNOWN_WAVE_FORMATS:
raise ValueError("Unknown wave file format")
# move file pointer to next chunk
if size > (bytes_read):
fid.read(size - bytes_read)
return (size, format_tag, channels, fs, bytes_per_second, block_align,
bit_depth)
# assumes file pointer is immediately after the 'data' id
def _read_data_chunk(fid, format_tag, channels, bit_depth, is_big_endian,
mmap=False):
if is_big_endian:
fmt = '>I'
else:
fmt = '<I'
# Size of the data subchunk in bytes
size = struct.unpack(fmt, fid.read(4))[0]
# Number of bytes per sample
bytes_per_sample = bit_depth//8
if bit_depth == 8:
dtype = 'u1'
else:
if is_big_endian:
dtype = '>'
else:
dtype = '<'
if format_tag == WAVE_FORMAT_PCM:
dtype += 'i%d' % bytes_per_sample
else:
dtype += 'f%d' % bytes_per_sample
if not mmap:
data = numpy.frombuffer(fid.read(size), dtype=dtype)
else:
start = fid.tell()
data = numpy.memmap(fid, dtype=dtype, mode='c', offset=start,
shape=(size//bytes_per_sample,))
fid.seek(start + size)
if channels > 1:
data = data.reshape(-1, channels)
return data
def _skip_unknown_chunk(fid, is_big_endian):
if is_big_endian:
fmt = '>I'
else:
fmt = '<I'
data = fid.read(4)
# call unpack() and seek() only if we have really read data from file
# otherwise empty read at the end of the file would trigger
# unnecessary exception at unpack() call
# in case data equals somehow to 0, there is no need for seek() anyway
if data:
size = struct.unpack(fmt, data)[0]
fid.seek(size, 1)
def _read_riff_chunk(fid):
str1 = fid.read(4) # File signature
if str1 == b'RIFF':
is_big_endian = False
fmt = '<I'
elif str1 == b'RIFX':
is_big_endian = True
fmt = '>I'
else:
# There are also .wav files with "FFIR" or "XFIR" signatures?
raise ValueError("File format {}... not "
"understood.".format(repr(str1)))
# Size of entire file
file_size = struct.unpack(fmt, fid.read(4))[0] + 8
str2 = fid.read(4)
if str2 != b'WAVE':
raise ValueError("Not a WAV file.")
return file_size, is_big_endian
def read(filename, mmap=False):
"""
Open a WAV file
Return the sample rate (in samples/sec) and data from a WAV file.
Parameters
----------
filename : string or open file handle
Input wav file.
mmap : bool, optional
Whether to read data as memory-mapped.
Only to be used on real files (Default: False).
.. versionadded:: 0.12.0
Returns
-------
rate : int
Sample rate of wav file.
data : numpy array
Data read from wav file. Data-type is determined from the file;
see Notes.
Notes
-----
This function cannot read wav files with 24-bit data.
Common data types: [1]_
===================== =========== =========== =============
WAV format Min Max NumPy dtype
===================== =========== =========== =============
32-bit floating-point -1.0 +1.0 float32
32-bit PCM -2147483648 +2147483647 int32
16-bit PCM -32768 +32767 int16
8-bit PCM 0 255 uint8
===================== =========== =========== =============
Note that 8-bit PCM is unsigned.
References
----------
.. [1] IBM Corporation and Microsoft Corporation, "Multimedia Programming
Interface and Data Specifications 1.0", section "Data Format of the
Samples", August 1991
http://www.tactilemedia.com/info/MCI_Control_Info.html
"""
if hasattr(filename, 'read'):
fid = filename
mmap = False
else:
fid = open(filename, 'rb')
try:
file_size, is_big_endian = _read_riff_chunk(fid)
fmt_chunk_received = False
channels = 1
bit_depth = 8
format_tag = WAVE_FORMAT_PCM
while fid.tell() < file_size:
# read the next chunk
chunk_id = fid.read(4)
if not chunk_id:
raise ValueError("Unexpected end of file.")
elif len(chunk_id) < 4:
raise ValueError("Incomplete wav chunk.")
if chunk_id == b'fmt ':
fmt_chunk_received = True
fmt_chunk = _read_fmt_chunk(fid, is_big_endian)
format_tag, channels, fs = fmt_chunk[1:4]
bit_depth = fmt_chunk[6]
if bit_depth not in (8, 16, 32, 64, 96, 128):
raise ValueError("Unsupported bit depth: the wav file "
"has {}-bit data.".format(bit_depth))
elif chunk_id == b'fact':
_skip_unknown_chunk(fid, is_big_endian)
elif chunk_id == b'data':
if not fmt_chunk_received:
raise ValueError("No fmt chunk before data")
data = _read_data_chunk(fid, format_tag, channels, bit_depth,
is_big_endian, mmap)
elif chunk_id == b'LIST':
# Someday this could be handled properly but for now skip it
_skip_unknown_chunk(fid, is_big_endian)
elif chunk_id in (b'JUNK', b'Fake'):
# Skip alignment chunks without warning
_skip_unknown_chunk(fid, is_big_endian)
else:
warnings.warn("Chunk (non-data) not understood, skipping it.",
WavFileWarning)
_skip_unknown_chunk(fid, is_big_endian)
finally:
if not hasattr(filename, 'read'):
fid.close()
else:
fid.seek(0)
return fs, data
def write(filename, rate, data):
"""
Write a numpy array as a WAV file.
Parameters
----------
filename : string or open file handle
Output wav file.
rate : int
The sample rate (in samples/sec).
data : ndarray
A 1-D or 2-D numpy array of either integer or float data-type.
Notes
-----
* Writes a simple uncompressed WAV file.
* To write multiple-channels, use a 2-D array of shape
(Nsamples, Nchannels).
* The bits-per-sample and PCM/float will be determined by the data-type.
Common data types: [1]_
===================== =========== =========== =============
WAV format Min Max NumPy dtype
===================== =========== =========== =============
32-bit floating-point -1.0 +1.0 float32
32-bit PCM -2147483648 +2147483647 int32
16-bit PCM -32768 +32767 int16
8-bit PCM 0 255 uint8
===================== =========== =========== =============
Note that 8-bit PCM is unsigned.
References
----------
.. [1] IBM Corporation and Microsoft Corporation, "Multimedia Programming
Interface and Data Specifications 1.0", section "Data Format of the
Samples", August 1991
http://www.tactilemedia.com/info/MCI_Control_Info.html
"""
if hasattr(filename, 'write'):
fid = filename
else:
fid = open(filename, 'wb')
fs = rate
try:
dkind = data.dtype.kind
if not (dkind == 'i' or dkind == 'f' or (dkind == 'u' and
data.dtype.itemsize == 1)):
raise ValueError("Unsupported data type '%s'" % data.dtype)
header_data = b''
header_data += b'RIFF'
header_data += b'\x00\x00\x00\x00'
header_data += b'WAVE'
# fmt chunk
header_data += b'fmt '
if dkind == 'f':
format_tag = WAVE_FORMAT_IEEE_FLOAT
else:
format_tag = WAVE_FORMAT_PCM
if data.ndim == 1:
channels = 1
else:
channels = data.shape[1]
bit_depth = data.dtype.itemsize * 8
bytes_per_second = fs*(bit_depth // 8)*channels
block_align = channels * (bit_depth // 8)
fmt_chunk_data = struct.pack('<HHIIHH', format_tag, channels, fs,
bytes_per_second, block_align, bit_depth)
if not (dkind == 'i' or dkind == 'u'):
# add cbSize field for non-PCM files
fmt_chunk_data += b'\x00\x00'
header_data += struct.pack('<I', len(fmt_chunk_data))
header_data += fmt_chunk_data
# fact chunk (non-PCM files)
if not (dkind == 'i' or dkind == 'u'):
header_data += b'fact'
header_data += struct.pack('<II', 4, data.shape[0])
# check data size (needs to be immediately before the data chunk)
if ((len(header_data)-4-4) + (4+4+data.nbytes)) > 0xFFFFFFFF:
raise ValueError("Data exceeds wave file size limit")
fid.write(header_data)
# data chunk
fid.write(b'data')
fid.write(struct.pack('<I', data.nbytes))
if data.dtype.byteorder == '>' or (data.dtype.byteorder == '=' and
sys.byteorder == 'big'):
data = data.byteswap()
_array_tofile(fid, data)
# Determine file size and place it in correct
# position at start of the file.
size = fid.tell()
fid.seek(4)
fid.write(struct.pack('<I', size-8))
finally:
if not hasattr(filename, 'write'):
fid.close()
else:
fid.seek(0)
if sys.version_info[0] >= 3:
def _array_tofile(fid, data):
# ravel gives a c-contiguous buffer
fid.write(data.ravel().view('b').data)
else:
def _array_tofile(fid, data):
fid.write(data.tostring())
| 12,547 | 29.906404 | 78 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/idl.py
|
# IDLSave - a python module to read IDL 'save' files
# Copyright (c) 2010 Thomas P. Robitaille
# Many thanks to Craig Markwardt for publishing the Unofficial Format
# Specification for IDL .sav files, without which this Python module would not
# exist (http://cow.physics.wisc.edu/~craigm/idl/savefmt).
# This code was developed by with permission from ITT Visual Information
# Systems. IDL(r) is a registered trademark of ITT Visual Information Systems,
# Inc. for their Interactive Data Language software.
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the "Software"),
# to deal in the Software without restriction, including without limitation
# the rights to use, copy, modify, merge, publish, distribute, sublicense,
# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.
from __future__ import division, print_function, absolute_import
import struct
import numpy as np
from numpy.compat import asstr
import tempfile
import zlib
import warnings
# Define the different data types that can be found in an IDL save file
DTYPE_DICT = {1: '>u1',
2: '>i2',
3: '>i4',
4: '>f4',
5: '>f8',
6: '>c8',
7: '|O',
8: '|O',
9: '>c16',
10: '|O',
11: '|O',
12: '>u2',
13: '>u4',
14: '>i8',
15: '>u8'}
# Define the different record types that can be found in an IDL save file
RECTYPE_DICT = {0: "START_MARKER",
1: "COMMON_VARIABLE",
2: "VARIABLE",
3: "SYSTEM_VARIABLE",
6: "END_MARKER",
10: "TIMESTAMP",
12: "COMPILED",
13: "IDENTIFICATION",
14: "VERSION",
15: "HEAP_HEADER",
16: "HEAP_DATA",
17: "PROMOTE64",
19: "NOTICE",
20: "DESCRIPTION"}
# Define a dictionary to contain structure definitions
STRUCT_DICT = {}
def _align_32(f):
'''Align to the next 32-bit position in a file'''
pos = f.tell()
if pos % 4 != 0:
f.seek(pos + 4 - pos % 4)
return
def _skip_bytes(f, n):
'''Skip `n` bytes'''
f.read(n)
return
def _read_bytes(f, n):
'''Read the next `n` bytes'''
return f.read(n)
def _read_byte(f):
'''Read a single byte'''
return np.uint8(struct.unpack('>B', f.read(4)[:1])[0])
def _read_long(f):
'''Read a signed 32-bit integer'''
return np.int32(struct.unpack('>l', f.read(4))[0])
def _read_int16(f):
'''Read a signed 16-bit integer'''
return np.int16(struct.unpack('>h', f.read(4)[2:4])[0])
def _read_int32(f):
'''Read a signed 32-bit integer'''
return np.int32(struct.unpack('>i', f.read(4))[0])
def _read_int64(f):
'''Read a signed 64-bit integer'''
return np.int64(struct.unpack('>q', f.read(8))[0])
def _read_uint16(f):
'''Read an unsigned 16-bit integer'''
return np.uint16(struct.unpack('>H', f.read(4)[2:4])[0])
def _read_uint32(f):
'''Read an unsigned 32-bit integer'''
return np.uint32(struct.unpack('>I', f.read(4))[0])
def _read_uint64(f):
'''Read an unsigned 64-bit integer'''
return np.uint64(struct.unpack('>Q', f.read(8))[0])
def _read_float32(f):
'''Read a 32-bit float'''
return np.float32(struct.unpack('>f', f.read(4))[0])
def _read_float64(f):
'''Read a 64-bit float'''
return np.float64(struct.unpack('>d', f.read(8))[0])
class Pointer(object):
'''Class used to define pointers'''
def __init__(self, index):
self.index = index
return
class ObjectPointer(Pointer):
'''Class used to define object pointers'''
pass
def _read_string(f):
'''Read a string'''
length = _read_long(f)
if length > 0:
chars = _read_bytes(f, length)
_align_32(f)
chars = asstr(chars)
else:
chars = ''
return chars
def _read_string_data(f):
'''Read a data string (length is specified twice)'''
length = _read_long(f)
if length > 0:
length = _read_long(f)
string_data = _read_bytes(f, length)
_align_32(f)
else:
string_data = ''
return string_data
def _read_data(f, dtype):
'''Read a variable with a specified data type'''
if dtype == 1:
if _read_int32(f) != 1:
raise Exception("Error occurred while reading byte variable")
return _read_byte(f)
elif dtype == 2:
return _read_int16(f)
elif dtype == 3:
return _read_int32(f)
elif dtype == 4:
return _read_float32(f)
elif dtype == 5:
return _read_float64(f)
elif dtype == 6:
real = _read_float32(f)
imag = _read_float32(f)
return np.complex64(real + imag * 1j)
elif dtype == 7:
return _read_string_data(f)
elif dtype == 8:
raise Exception("Should not be here - please report this")
elif dtype == 9:
real = _read_float64(f)
imag = _read_float64(f)
return np.complex128(real + imag * 1j)
elif dtype == 10:
return Pointer(_read_int32(f))
elif dtype == 11:
return ObjectPointer(_read_int32(f))
elif dtype == 12:
return _read_uint16(f)
elif dtype == 13:
return _read_uint32(f)
elif dtype == 14:
return _read_int64(f)
elif dtype == 15:
return _read_uint64(f)
else:
raise Exception("Unknown IDL type: %i - please report this" % dtype)
def _read_structure(f, array_desc, struct_desc):
'''
Read a structure, with the array and structure descriptors given as
`array_desc` and `structure_desc` respectively.
'''
nrows = array_desc['nelements']
columns = struct_desc['tagtable']
dtype = []
for col in columns:
if col['structure'] or col['array']:
dtype.append(((col['name'].lower(), col['name']), np.object_))
else:
if col['typecode'] in DTYPE_DICT:
dtype.append(((col['name'].lower(), col['name']),
DTYPE_DICT[col['typecode']]))
else:
raise Exception("Variable type %i not implemented" %
col['typecode'])
structure = np.recarray((nrows, ), dtype=dtype)
for i in range(nrows):
for col in columns:
dtype = col['typecode']
if col['structure']:
structure[col['name']][i] = _read_structure(f,
struct_desc['arrtable'][col['name']],
struct_desc['structtable'][col['name']])
elif col['array']:
structure[col['name']][i] = _read_array(f, dtype,
struct_desc['arrtable'][col['name']])
else:
structure[col['name']][i] = _read_data(f, dtype)
# Reshape structure if needed
if array_desc['ndims'] > 1:
dims = array_desc['dims'][:int(array_desc['ndims'])]
dims.reverse()
structure = structure.reshape(dims)
return structure
def _read_array(f, typecode, array_desc):
'''
Read an array of type `typecode`, with the array descriptor given as
`array_desc`.
'''
if typecode in [1, 3, 4, 5, 6, 9, 13, 14, 15]:
if typecode == 1:
nbytes = _read_int32(f)
if nbytes != array_desc['nbytes']:
warnings.warn("Not able to verify number of bytes from header")
# Read bytes as numpy array
array = np.frombuffer(f.read(array_desc['nbytes']),
dtype=DTYPE_DICT[typecode])
elif typecode in [2, 12]:
# These are 2 byte types, need to skip every two as they are not packed
array = np.frombuffer(f.read(array_desc['nbytes']*2),
dtype=DTYPE_DICT[typecode])[1::2]
else:
# Read bytes into list
array = []
for i in range(array_desc['nelements']):
dtype = typecode
data = _read_data(f, dtype)
array.append(data)
array = np.array(array, dtype=np.object_)
# Reshape array if needed
if array_desc['ndims'] > 1:
dims = array_desc['dims'][:int(array_desc['ndims'])]
dims.reverse()
array = array.reshape(dims)
# Go to next alignment position
_align_32(f)
return array
def _read_record(f):
'''Function to read in a full record'''
record = {'rectype': _read_long(f)}
nextrec = _read_uint32(f)
nextrec += _read_uint32(f) * 2**32
_skip_bytes(f, 4)
if not record['rectype'] in RECTYPE_DICT:
raise Exception("Unknown RECTYPE: %i" % record['rectype'])
record['rectype'] = RECTYPE_DICT[record['rectype']]
if record['rectype'] in ["VARIABLE", "HEAP_DATA"]:
if record['rectype'] == "VARIABLE":
record['varname'] = _read_string(f)
else:
record['heap_index'] = _read_long(f)
_skip_bytes(f, 4)
rectypedesc = _read_typedesc(f)
if rectypedesc['typecode'] == 0:
if nextrec == f.tell():
record['data'] = None # Indicates NULL value
else:
raise ValueError("Unexpected type code: 0")
else:
varstart = _read_long(f)
if varstart != 7:
raise Exception("VARSTART is not 7")
if rectypedesc['structure']:
record['data'] = _read_structure(f, rectypedesc['array_desc'],
rectypedesc['struct_desc'])
elif rectypedesc['array']:
record['data'] = _read_array(f, rectypedesc['typecode'],
rectypedesc['array_desc'])
else:
dtype = rectypedesc['typecode']
record['data'] = _read_data(f, dtype)
elif record['rectype'] == "TIMESTAMP":
_skip_bytes(f, 4*256)
record['date'] = _read_string(f)
record['user'] = _read_string(f)
record['host'] = _read_string(f)
elif record['rectype'] == "VERSION":
record['format'] = _read_long(f)
record['arch'] = _read_string(f)
record['os'] = _read_string(f)
record['release'] = _read_string(f)
elif record['rectype'] == "IDENTIFICATON":
record['author'] = _read_string(f)
record['title'] = _read_string(f)
record['idcode'] = _read_string(f)
elif record['rectype'] == "NOTICE":
record['notice'] = _read_string(f)
elif record['rectype'] == "DESCRIPTION":
record['description'] = _read_string_data(f)
elif record['rectype'] == "HEAP_HEADER":
record['nvalues'] = _read_long(f)
record['indices'] = []
for i in range(record['nvalues']):
record['indices'].append(_read_long(f))
elif record['rectype'] == "COMMONBLOCK":
record['nvars'] = _read_long(f)
record['name'] = _read_string(f)
record['varnames'] = []
for i in range(record['nvars']):
record['varnames'].append(_read_string(f))
elif record['rectype'] == "END_MARKER":
record['end'] = True
elif record['rectype'] == "UNKNOWN":
warnings.warn("Skipping UNKNOWN record")
elif record['rectype'] == "SYSTEM_VARIABLE":
warnings.warn("Skipping SYSTEM_VARIABLE record")
else:
raise Exception("record['rectype']=%s not implemented" %
record['rectype'])
f.seek(nextrec)
return record
def _read_typedesc(f):
'''Function to read in a type descriptor'''
typedesc = {'typecode': _read_long(f), 'varflags': _read_long(f)}
if typedesc['varflags'] & 2 == 2:
raise Exception("System variables not implemented")
typedesc['array'] = typedesc['varflags'] & 4 == 4
typedesc['structure'] = typedesc['varflags'] & 32 == 32
if typedesc['structure']:
typedesc['array_desc'] = _read_arraydesc(f)
typedesc['struct_desc'] = _read_structdesc(f)
elif typedesc['array']:
typedesc['array_desc'] = _read_arraydesc(f)
return typedesc
def _read_arraydesc(f):
'''Function to read in an array descriptor'''
arraydesc = {'arrstart': _read_long(f)}
if arraydesc['arrstart'] == 8:
_skip_bytes(f, 4)
arraydesc['nbytes'] = _read_long(f)
arraydesc['nelements'] = _read_long(f)
arraydesc['ndims'] = _read_long(f)
_skip_bytes(f, 8)
arraydesc['nmax'] = _read_long(f)
arraydesc['dims'] = []
for d in range(arraydesc['nmax']):
arraydesc['dims'].append(_read_long(f))
elif arraydesc['arrstart'] == 18:
warnings.warn("Using experimental 64-bit array read")
_skip_bytes(f, 8)
arraydesc['nbytes'] = _read_uint64(f)
arraydesc['nelements'] = _read_uint64(f)
arraydesc['ndims'] = _read_long(f)
_skip_bytes(f, 8)
arraydesc['nmax'] = 8
arraydesc['dims'] = []
for d in range(arraydesc['nmax']):
v = _read_long(f)
if v != 0:
raise Exception("Expected a zero in ARRAY_DESC")
arraydesc['dims'].append(_read_long(f))
else:
raise Exception("Unknown ARRSTART: %i" % arraydesc['arrstart'])
return arraydesc
def _read_structdesc(f):
'''Function to read in a structure descriptor'''
structdesc = {}
structstart = _read_long(f)
if structstart != 9:
raise Exception("STRUCTSTART should be 9")
structdesc['name'] = _read_string(f)
predef = _read_long(f)
structdesc['ntags'] = _read_long(f)
structdesc['nbytes'] = _read_long(f)
structdesc['predef'] = predef & 1
structdesc['inherits'] = predef & 2
structdesc['is_super'] = predef & 4
if not structdesc['predef']:
structdesc['tagtable'] = []
for t in range(structdesc['ntags']):
structdesc['tagtable'].append(_read_tagdesc(f))
for tag in structdesc['tagtable']:
tag['name'] = _read_string(f)
structdesc['arrtable'] = {}
for tag in structdesc['tagtable']:
if tag['array']:
structdesc['arrtable'][tag['name']] = _read_arraydesc(f)
structdesc['structtable'] = {}
for tag in structdesc['tagtable']:
if tag['structure']:
structdesc['structtable'][tag['name']] = _read_structdesc(f)
if structdesc['inherits'] or structdesc['is_super']:
structdesc['classname'] = _read_string(f)
structdesc['nsupclasses'] = _read_long(f)
structdesc['supclassnames'] = []
for s in range(structdesc['nsupclasses']):
structdesc['supclassnames'].append(_read_string(f))
structdesc['supclasstable'] = []
for s in range(structdesc['nsupclasses']):
structdesc['supclasstable'].append(_read_structdesc(f))
STRUCT_DICT[structdesc['name']] = structdesc
else:
if not structdesc['name'] in STRUCT_DICT:
raise Exception("PREDEF=1 but can't find definition")
structdesc = STRUCT_DICT[structdesc['name']]
return structdesc
def _read_tagdesc(f):
'''Function to read in a tag descriptor'''
tagdesc = {'offset': _read_long(f)}
if tagdesc['offset'] == -1:
tagdesc['offset'] = _read_uint64(f)
tagdesc['typecode'] = _read_long(f)
tagflags = _read_long(f)
tagdesc['array'] = tagflags & 4 == 4
tagdesc['structure'] = tagflags & 32 == 32
tagdesc['scalar'] = tagdesc['typecode'] in DTYPE_DICT
# Assume '10'x is scalar
return tagdesc
def _replace_heap(variable, heap):
if isinstance(variable, Pointer):
while isinstance(variable, Pointer):
if variable.index == 0:
variable = None
else:
if variable.index in heap:
variable = heap[variable.index]
else:
warnings.warn("Variable referenced by pointer not found "
"in heap: variable will be set to None")
variable = None
replace, new = _replace_heap(variable, heap)
if replace:
variable = new
return True, variable
elif isinstance(variable, np.core.records.recarray):
# Loop over records
for ir, record in enumerate(variable):
replace, new = _replace_heap(record, heap)
if replace:
variable[ir] = new
return False, variable
elif isinstance(variable, np.core.records.record):
# Loop over values
for iv, value in enumerate(variable):
replace, new = _replace_heap(value, heap)
if replace:
variable[iv] = new
return False, variable
elif isinstance(variable, np.ndarray):
# Loop over values if type is np.object_
if variable.dtype.type is np.object_:
for iv in range(variable.size):
replace, new = _replace_heap(variable.item(iv), heap)
if replace:
variable.itemset(iv, new)
return False, variable
else:
return False, variable
class AttrDict(dict):
'''
A case-insensitive dictionary with access via item, attribute, and call
notations:
>>> d = AttrDict()
>>> d['Variable'] = 123
>>> d['Variable']
123
>>> d.Variable
123
>>> d.variable
123
>>> d('VARIABLE')
123
'''
def __init__(self, init={}):
dict.__init__(self, init)
def __getitem__(self, name):
return super(AttrDict, self).__getitem__(name.lower())
def __setitem__(self, key, value):
return super(AttrDict, self).__setitem__(key.lower(), value)
__getattr__ = __getitem__
__setattr__ = __setitem__
__call__ = __getitem__
def readsav(file_name, idict=None, python_dict=False,
uncompressed_file_name=None, verbose=False):
"""
Read an IDL .sav file.
Parameters
----------
file_name : str
Name of the IDL save file.
idict : dict, optional
Dictionary in which to insert .sav file variables.
python_dict : bool, optional
By default, the object return is not a Python dictionary, but a
case-insensitive dictionary with item, attribute, and call access
to variables. To get a standard Python dictionary, set this option
to True.
uncompressed_file_name : str, optional
This option only has an effect for .sav files written with the
/compress option. If a file name is specified, compressed .sav
files are uncompressed to this file. Otherwise, readsav will use
the `tempfile` module to determine a temporary filename
automatically, and will remove the temporary file upon successfully
reading it in.
verbose : bool, optional
Whether to print out information about the save file, including
the records read, and available variables.
Returns
-------
idl_dict : AttrDict or dict
If `python_dict` is set to False (default), this function returns a
case-insensitive dictionary with item, attribute, and call access
to variables. If `python_dict` is set to True, this function
returns a Python dictionary with all variable names in lowercase.
If `idict` was specified, then variables are written to the
dictionary specified, and the updated dictionary is returned.
"""
# Initialize record and variable holders
records = []
if python_dict or idict:
variables = {}
else:
variables = AttrDict()
# Open the IDL file
f = open(file_name, 'rb')
# Read the signature, which should be 'SR'
signature = _read_bytes(f, 2)
if signature != b'SR':
raise Exception("Invalid SIGNATURE: %s" % signature)
# Next, the record format, which is '\x00\x04' for normal .sav
# files, and '\x00\x06' for compressed .sav files.
recfmt = _read_bytes(f, 2)
if recfmt == b'\x00\x04':
pass
elif recfmt == b'\x00\x06':
if verbose:
print("IDL Save file is compressed")
if uncompressed_file_name:
fout = open(uncompressed_file_name, 'w+b')
else:
fout = tempfile.NamedTemporaryFile(suffix='.sav')
if verbose:
print(" -> expanding to %s" % fout.name)
# Write header
fout.write(b'SR\x00\x04')
# Cycle through records
while True:
# Read record type
rectype = _read_long(f)
fout.write(struct.pack('>l', int(rectype)))
# Read position of next record and return as int
nextrec = _read_uint32(f)
nextrec += _read_uint32(f) * 2**32
# Read the unknown 4 bytes
unknown = f.read(4)
# Check if the end of the file has been reached
if RECTYPE_DICT[rectype] == 'END_MARKER':
fout.write(struct.pack('>I', int(nextrec) % 2**32))
fout.write(struct.pack('>I', int((nextrec - (nextrec % 2**32)) / 2**32)))
fout.write(unknown)
break
# Find current position
pos = f.tell()
# Decompress record
rec_string = zlib.decompress(f.read(nextrec-pos))
# Find new position of next record
nextrec = fout.tell() + len(rec_string) + 12
# Write out record
fout.write(struct.pack('>I', int(nextrec % 2**32)))
fout.write(struct.pack('>I', int((nextrec - (nextrec % 2**32)) / 2**32)))
fout.write(unknown)
fout.write(rec_string)
# Close the original compressed file
f.close()
# Set f to be the decompressed file, and skip the first four bytes
f = fout
f.seek(4)
else:
raise Exception("Invalid RECFMT: %s" % recfmt)
# Loop through records, and add them to the list
while True:
r = _read_record(f)
records.append(r)
if 'end' in r:
if r['end']:
break
# Close the file
f.close()
# Find heap data variables
heap = {}
for r in records:
if r['rectype'] == "HEAP_DATA":
heap[r['heap_index']] = r['data']
# Find all variables
for r in records:
if r['rectype'] == "VARIABLE":
replace, new = _replace_heap(r['data'], heap)
if replace:
r['data'] = new
variables[r['varname'].lower()] = r['data']
if verbose:
# Print out timestamp info about the file
for record in records:
if record['rectype'] == "TIMESTAMP":
print("-"*50)
print("Date: %s" % record['date'])
print("User: %s" % record['user'])
print("Host: %s" % record['host'])
break
# Print out version info about the file
for record in records:
if record['rectype'] == "VERSION":
print("-"*50)
print("Format: %s" % record['format'])
print("Architecture: %s" % record['arch'])
print("Operating System: %s" % record['os'])
print("IDL Version: %s" % record['release'])
break
# Print out identification info about the file
for record in records:
if record['rectype'] == "IDENTIFICATON":
print("-"*50)
print("Author: %s" % record['author'])
print("Title: %s" % record['title'])
print("ID Code: %s" % record['idcode'])
break
# Print out descriptions saved with the file
for record in records:
if record['rectype'] == "DESCRIPTION":
print("-"*50)
print("Description: %s" % record['description'])
break
print("-"*50)
print("Successfully read %i records of which:" %
(len(records)))
# Create convenience list of record types
rectypes = [r['rectype'] for r in records]
for rt in set(rectypes):
if rt != 'END_MARKER':
print(" - %i are of type %s" % (rectypes.count(rt), rt))
print("-"*50)
if 'VARIABLE' in rectypes:
print("Available variables:")
for var in variables:
print(" - %s [%s]" % (var, type(variables[var])))
print("-"*50)
if idict:
for var in variables:
idict[var] = variables[var]
return idict
else:
return variables
| 25,814 | 28.235561 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/__init__.py
|
# -*- encoding:utf-8 -*-
"""
==================================
Input and output (:mod:`scipy.io`)
==================================
.. currentmodule:: scipy.io
SciPy has many modules, classes, and functions available to read data
from and write data to a variety of file formats.
.. seealso:: :ref:`numpy-reference.routines.io` (in Numpy)
MATLAB® files
=============
.. autosummary::
:toctree: generated/
loadmat - Read a MATLAB style mat file (version 4 through 7.1)
savemat - Write a MATLAB style mat file (version 4 through 7.1)
whosmat - List contents of a MATLAB style mat file (version 4 through 7.1)
IDL® files
==========
.. autosummary::
:toctree: generated/
readsav - Read an IDL 'save' file
Matrix Market files
===================
.. autosummary::
:toctree: generated/
mminfo - Query matrix info from Matrix Market formatted file
mmread - Read matrix from Matrix Market formatted file
mmwrite - Write matrix to Matrix Market formatted file
Unformatted Fortran files
===============================
.. autosummary::
:toctree: generated/
FortranFile - A file object for unformatted sequential Fortran files
Netcdf
======
.. autosummary::
:toctree: generated/
netcdf_file - A file object for NetCDF data
netcdf_variable - A data object for the netcdf module
Harwell-Boeing files
====================
.. autosummary::
:toctree: generated/
hb_read -- read H-B file
hb_write -- write H-B file
Wav sound files (:mod:`scipy.io.wavfile`)
=========================================
.. module:: scipy.io.wavfile
.. autosummary::
:toctree: generated/
read
write
WavFileWarning
Arff files (:mod:`scipy.io.arff`)
=================================
.. module:: scipy.io.arff
.. autosummary::
:toctree: generated/
loadarff
MetaData
ArffError
ParseArffError
"""
from __future__ import division, print_function, absolute_import
# matfile read and write
from .matlab import loadmat, savemat, whosmat, byteordercodes
# netCDF file support
from .netcdf import netcdf_file, netcdf_variable
# Fortran file support
from ._fortran import FortranFile
from .mmio import mminfo, mmread, mmwrite
from .idl import readsav
from .harwell_boeing import hb_read, hb_write
__all__ = [s for s in dir() if not s.startswith('_')]
from scipy._lib._testutils import PytestTester
test = PytestTester(__name__)
del PytestTester
| 2,416 | 20.201754 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/byteordercodes.py
|
''' Byteorder utilities for system - numpy byteorder encoding
Converts a variety of string codes for little endian, big endian,
native byte order and swapped byte order to explicit numpy endian
codes - one of '<' (little endian) or '>' (big endian)
'''
from __future__ import division, print_function, absolute_import
import sys
sys_is_le = sys.byteorder == 'little'
native_code = sys_is_le and '<' or '>'
swapped_code = sys_is_le and '>' or '<'
aliases = {'little': ('little', '<', 'l', 'le'),
'big': ('big', '>', 'b', 'be'),
'native': ('native', '='),
'swapped': ('swapped', 'S')}
def to_numpy_code(code):
"""
Convert various order codings to numpy format.
Parameters
----------
code : str
The code to convert. It is converted to lower case before parsing.
Legal values are:
'little', 'big', 'l', 'b', 'le', 'be', '<', '>', 'native', '=',
'swapped', 's'.
Returns
-------
out_code : {'<', '>'}
Here '<' is the numpy dtype code for little endian,
and '>' is the code for big endian.
Examples
--------
>>> import sys
>>> sys_is_le == (sys.byteorder == 'little')
True
>>> to_numpy_code('big')
'>'
>>> to_numpy_code('little')
'<'
>>> nc = to_numpy_code('native')
>>> nc == '<' if sys_is_le else nc == '>'
True
>>> sc = to_numpy_code('swapped')
>>> sc == '>' if sys_is_le else sc == '<'
True
"""
code = code.lower()
if code is None:
return native_code
if code in aliases['little']:
return '<'
elif code in aliases['big']:
return '>'
elif code in aliases['native']:
return native_code
elif code in aliases['swapped']:
return swapped_code
else:
raise ValueError(
'We cannot handle byte order %s' % code)
| 1,874 | 25.408451 | 74 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/mio5.py
|
''' Classes for read / write of matlab (TM) 5 files
The matfile specification last found here:
http://www.mathworks.com/access/helpdesk/help/pdf_doc/matlab/matfile_format.pdf
(as of December 5 2008)
'''
from __future__ import division, print_function, absolute_import
'''
=================================
Note on functions and mat files
=================================
The document above does not give any hints as to the storage of matlab
function handles, or anonymous function handles. I had therefore to
guess the format of matlab arrays of ``mxFUNCTION_CLASS`` and
``mxOPAQUE_CLASS`` by looking at example mat files.
``mxFUNCTION_CLASS`` stores all types of matlab functions. It seems to
contain a struct matrix with a set pattern of fields. For anonymous
functions, a sub-fields of one of these fields seems to contain the
well-named ``mxOPAQUE_CLASS``. This seems to cotain:
* array flags as for any matlab matrix
* 3 int8 strings
* a matrix
It seems that, whenever the mat file contains a ``mxOPAQUE_CLASS``
instance, there is also an un-named matrix (name == '') at the end of
the mat file. I'll call this the ``__function_workspace__`` matrix.
When I saved two anonymous functions in a mat file, or appended another
anonymous function to the mat file, there was still only one
``__function_workspace__`` un-named matrix at the end, but larger than
that for a mat file with a single anonymous function, suggesting that
the workspaces for the two functions had been merged.
The ``__function_workspace__`` matrix appears to be of double class
(``mxCLASS_DOUBLE``), but stored as uint8, the memory for which is in
the format of a mini .mat file, without the first 124 bytes of the file
header (the description and the subsystem_offset), but with the version
U2 bytes, and the S2 endian test bytes. There follow 4 zero bytes,
presumably for 8 byte padding, and then a series of ``miMATRIX``
entries, as in a standard mat file. The ``miMATRIX`` entries appear to
be series of un-named (name == '') matrices, and may also contain arrays
of this same mini-mat format.
I guess that:
* saving an anonymous function back to a mat file will need the
associated ``__function_workspace__`` matrix saved as well for the
anonymous function to work correctly.
* appending to a mat file that has a ``__function_workspace__`` would
involve first pulling off this workspace, appending, checking whether
there were any more anonymous functions appended, and then somehow
merging the relevant workspaces, and saving at the end of the mat
file.
The mat files I was playing with are in ``tests/data``:
* sqr.mat
* parabola.mat
* some_functions.mat
See ``tests/test_mio.py:test_mio_funcs.py`` for a debugging
script I was working with.
'''
# Small fragments of current code adapted from matfile.py by Heiko
# Henkelmann
import os
import time
import sys
import zlib
from io import BytesIO
import warnings
import numpy as np
from numpy.compat import asbytes, asstr
import scipy.sparse
from scipy._lib.six import string_types
from .byteordercodes import native_code, swapped_code
from .miobase import (MatFileReader, docfiller, matdims, read_dtype,
arr_to_chars, arr_dtype_number, MatWriteError,
MatReadError, MatReadWarning)
# Reader object for matlab 5 format variables
from .mio5_utils import VarReader5
# Constants and helper objects
from .mio5_params import (MatlabObject, MatlabFunction, MDTYPES, NP_TO_MTYPES,
NP_TO_MXTYPES, miCOMPRESSED, miMATRIX, miINT8,
miUTF8, miUINT32, mxCELL_CLASS, mxSTRUCT_CLASS,
mxOBJECT_CLASS, mxCHAR_CLASS, mxSPARSE_CLASS,
mxDOUBLE_CLASS, mclass_info)
from .streams import ZlibInputStream
class MatFile5Reader(MatFileReader):
''' Reader for Mat 5 mat files
Adds the following attribute to base class
uint16_codec - char codec to use for uint16 char arrays
(defaults to system default codec)
Uses variable reader that has the following stardard interface (see
abstract class in ``miobase``::
__init__(self, file_reader)
read_header(self)
array_from_header(self)
and added interface::
set_stream(self, stream)
read_full_tag(self)
'''
@docfiller
def __init__(self,
mat_stream,
byte_order=None,
mat_dtype=False,
squeeze_me=False,
chars_as_strings=True,
matlab_compatible=False,
struct_as_record=True,
verify_compressed_data_integrity=True,
uint16_codec=None
):
'''Initializer for matlab 5 file format reader
%(matstream_arg)s
%(load_args)s
%(struct_arg)s
uint16_codec : {None, string}
Set codec to use for uint16 char arrays (e.g. 'utf-8').
Use system default codec if None
'''
super(MatFile5Reader, self).__init__(
mat_stream,
byte_order,
mat_dtype,
squeeze_me,
chars_as_strings,
matlab_compatible,
struct_as_record,
verify_compressed_data_integrity
)
# Set uint16 codec
if not uint16_codec:
uint16_codec = sys.getdefaultencoding()
self.uint16_codec = uint16_codec
# placeholders for readers - see initialize_read method
self._file_reader = None
self._matrix_reader = None
def guess_byte_order(self):
''' Guess byte order.
Sets stream pointer to 0 '''
self.mat_stream.seek(126)
mi = self.mat_stream.read(2)
self.mat_stream.seek(0)
return mi == b'IM' and '<' or '>'
def read_file_header(self):
''' Read in mat 5 file header '''
hdict = {}
hdr_dtype = MDTYPES[self.byte_order]['dtypes']['file_header']
hdr = read_dtype(self.mat_stream, hdr_dtype)
hdict['__header__'] = hdr['description'].item().strip(b' \t\n\000')
v_major = hdr['version'] >> 8
v_minor = hdr['version'] & 0xFF
hdict['__version__'] = '%d.%d' % (v_major, v_minor)
return hdict
def initialize_read(self):
''' Run when beginning read of variables
Sets up readers from parameters in `self`
'''
# reader for top level stream. We need this extra top-level
# reader because we use the matrix_reader object to contain
# compressed matrices (so they have their own stream)
self._file_reader = VarReader5(self)
# reader for matrix streams
self._matrix_reader = VarReader5(self)
def read_var_header(self):
''' Read header, return header, next position
Header has to define at least .name and .is_global
Parameters
----------
None
Returns
-------
header : object
object that can be passed to self.read_var_array, and that
has attributes .name and .is_global
next_position : int
position in stream of next variable
'''
mdtype, byte_count = self._file_reader.read_full_tag()
if not byte_count > 0:
raise ValueError("Did not read any bytes")
next_pos = self.mat_stream.tell() + byte_count
if mdtype == miCOMPRESSED:
# Make new stream from compressed data
stream = ZlibInputStream(self.mat_stream, byte_count)
self._matrix_reader.set_stream(stream)
check_stream_limit = self.verify_compressed_data_integrity
mdtype, byte_count = self._matrix_reader.read_full_tag()
else:
check_stream_limit = False
self._matrix_reader.set_stream(self.mat_stream)
if not mdtype == miMATRIX:
raise TypeError('Expecting miMATRIX type here, got %d' % mdtype)
header = self._matrix_reader.read_header(check_stream_limit)
return header, next_pos
def read_var_array(self, header, process=True):
''' Read array, given `header`
Parameters
----------
header : header object
object with fields defining variable header
process : {True, False} bool, optional
If True, apply recursive post-processing during loading of
array.
Returns
-------
arr : array
array with post-processing applied or not according to
`process`.
'''
return self._matrix_reader.array_from_header(header, process)
def get_variables(self, variable_names=None):
''' get variables from stream as dictionary
variable_names - optional list of variable names to get
If variable_names is None, then get all variables in file
'''
if isinstance(variable_names, string_types):
variable_names = [variable_names]
elif variable_names is not None:
variable_names = list(variable_names)
self.mat_stream.seek(0)
# Here we pass all the parameters in self to the reading objects
self.initialize_read()
mdict = self.read_file_header()
mdict['__globals__'] = []
while not self.end_of_stream():
hdr, next_position = self.read_var_header()
name = asstr(hdr.name)
if name in mdict:
warnings.warn('Duplicate variable name "%s" in stream'
' - replacing previous with new\n'
'Consider mio5.varmats_from_mat to split '
'file into single variable files' % name,
MatReadWarning, stacklevel=2)
if name == '':
# can only be a matlab 7 function workspace
name = '__function_workspace__'
# We want to keep this raw because mat_dtype processing
# will break the format (uint8 as mxDOUBLE_CLASS)
process = False
else:
process = True
if variable_names is not None and name not in variable_names:
self.mat_stream.seek(next_position)
continue
try:
res = self.read_var_array(hdr, process)
except MatReadError as err:
warnings.warn(
'Unreadable variable "%s", because "%s"' %
(name, err),
Warning, stacklevel=2)
res = "Read error: %s" % err
self.mat_stream.seek(next_position)
mdict[name] = res
if hdr.is_global:
mdict['__globals__'].append(name)
if variable_names is not None:
variable_names.remove(name)
if len(variable_names) == 0:
break
return mdict
def list_variables(self):
''' list variables from stream '''
self.mat_stream.seek(0)
# Here we pass all the parameters in self to the reading objects
self.initialize_read()
self.read_file_header()
vars = []
while not self.end_of_stream():
hdr, next_position = self.read_var_header()
name = asstr(hdr.name)
if name == '':
# can only be a matlab 7 function workspace
name = '__function_workspace__'
shape = self._matrix_reader.shape_from_header(hdr)
if hdr.is_logical:
info = 'logical'
else:
info = mclass_info.get(hdr.mclass, 'unknown')
vars.append((name, shape, info))
self.mat_stream.seek(next_position)
return vars
def varmats_from_mat(file_obj):
""" Pull variables out of mat 5 file as a sequence of mat file objects
This can be useful with a difficult mat file, containing unreadable
variables. This routine pulls the variables out in raw form and puts them,
unread, back into a file stream for saving or reading. Another use is the
pathological case where there is more than one variable of the same name in
the file; this routine returns the duplicates, whereas the standard reader
will overwrite duplicates in the returned dictionary.
The file pointer in `file_obj` will be undefined. File pointers for the
returned file-like objects are set at 0.
Parameters
----------
file_obj : file-like
file object containing mat file
Returns
-------
named_mats : list
list contains tuples of (name, BytesIO) where BytesIO is a file-like
object containing mat file contents as for a single variable. The
BytesIO contains a string with the original header and a single var. If
``var_file_obj`` is an individual BytesIO instance, then save as a mat
file with something like ``open('test.mat',
'wb').write(var_file_obj.read())``
Examples
--------
>>> import scipy.io
BytesIO is from the ``io`` module in python 3, and is ``cStringIO`` for
python < 3.
>>> mat_fileobj = BytesIO()
>>> scipy.io.savemat(mat_fileobj, {'b': np.arange(10), 'a': 'a string'})
>>> varmats = varmats_from_mat(mat_fileobj)
>>> sorted([name for name, str_obj in varmats])
['a', 'b']
"""
rdr = MatFile5Reader(file_obj)
file_obj.seek(0)
# Raw read of top-level file header
hdr_len = MDTYPES[native_code]['dtypes']['file_header'].itemsize
raw_hdr = file_obj.read(hdr_len)
# Initialize variable reading
file_obj.seek(0)
rdr.initialize_read()
mdict = rdr.read_file_header()
next_position = file_obj.tell()
named_mats = []
while not rdr.end_of_stream():
start_position = next_position
hdr, next_position = rdr.read_var_header()
name = asstr(hdr.name)
# Read raw variable string
file_obj.seek(start_position)
byte_count = next_position - start_position
var_str = file_obj.read(byte_count)
# write to stringio object
out_obj = BytesIO()
out_obj.write(raw_hdr)
out_obj.write(var_str)
out_obj.seek(0)
named_mats.append((name, out_obj))
return named_mats
class EmptyStructMarker(object):
""" Class to indicate presence of empty matlab struct on output """
def to_writeable(source):
''' Convert input object ``source`` to something we can write
Parameters
----------
source : object
Returns
-------
arr : None or ndarray or EmptyStructMarker
If `source` cannot be converted to something we can write to a matfile,
return None. If `source` is equivalent to an empty dictionary, return
``EmptyStructMarker``. Otherwise return `source` converted to an
ndarray with contents for writing to matfile.
'''
if isinstance(source, np.ndarray):
return source
if source is None:
return None
# Objects that implement mappings
is_mapping = (hasattr(source, 'keys') and hasattr(source, 'values') and
hasattr(source, 'items'))
# Objects that don't implement mappings, but do have dicts
if isinstance(source, np.generic):
# Numpy scalars are never mappings (pypy issue workaround)
pass
elif not is_mapping and hasattr(source, '__dict__'):
source = dict((key, value) for key, value in source.__dict__.items()
if not key.startswith('_'))
is_mapping = True
if is_mapping:
dtype = []
values = []
for field, value in source.items():
if (isinstance(field, string_types) and
field[0] not in '_0123456789'):
dtype.append((str(field), object))
values.append(value)
if dtype:
return np.array([tuple(values)], dtype)
else:
return EmptyStructMarker
# Next try and convert to an array
narr = np.asanyarray(source)
if narr.dtype.type in (object, np.object_) and \
narr.shape == () and narr == source:
# No interesting conversion possible
return None
return narr
# Native byte ordered dtypes for convenience for writers
NDT_FILE_HDR = MDTYPES[native_code]['dtypes']['file_header']
NDT_TAG_FULL = MDTYPES[native_code]['dtypes']['tag_full']
NDT_TAG_SMALL = MDTYPES[native_code]['dtypes']['tag_smalldata']
NDT_ARRAY_FLAGS = MDTYPES[native_code]['dtypes']['array_flags']
class VarWriter5(object):
''' Generic matlab matrix writing class '''
mat_tag = np.zeros((), NDT_TAG_FULL)
mat_tag['mdtype'] = miMATRIX
def __init__(self, file_writer):
self.file_stream = file_writer.file_stream
self.unicode_strings = file_writer.unicode_strings
self.long_field_names = file_writer.long_field_names
self.oned_as = file_writer.oned_as
# These are used for top level writes, and unset after
self._var_name = None
self._var_is_global = False
def write_bytes(self, arr):
self.file_stream.write(arr.tostring(order='F'))
def write_string(self, s):
self.file_stream.write(s)
def write_element(self, arr, mdtype=None):
''' write tag and data '''
if mdtype is None:
mdtype = NP_TO_MTYPES[arr.dtype.str[1:]]
# Array needs to be in native byte order
if arr.dtype.byteorder == swapped_code:
arr = arr.byteswap().newbyteorder()
byte_count = arr.size*arr.itemsize
if byte_count <= 4:
self.write_smalldata_element(arr, mdtype, byte_count)
else:
self.write_regular_element(arr, mdtype, byte_count)
def write_smalldata_element(self, arr, mdtype, byte_count):
# write tag with embedded data
tag = np.zeros((), NDT_TAG_SMALL)
tag['byte_count_mdtype'] = (byte_count << 16) + mdtype
# if arr.tostring is < 4, the element will be zero-padded as needed.
tag['data'] = arr.tostring(order='F')
self.write_bytes(tag)
def write_regular_element(self, arr, mdtype, byte_count):
# write tag, data
tag = np.zeros((), NDT_TAG_FULL)
tag['mdtype'] = mdtype
tag['byte_count'] = byte_count
self.write_bytes(tag)
self.write_bytes(arr)
# pad to next 64-bit boundary
bc_mod_8 = byte_count % 8
if bc_mod_8:
self.file_stream.write(b'\x00' * (8-bc_mod_8))
def write_header(self,
shape,
mclass,
is_complex=False,
is_logical=False,
nzmax=0):
''' Write header for given data options
shape : sequence
array shape
mclass - mat5 matrix class
is_complex - True if matrix is complex
is_logical - True if matrix is logical
nzmax - max non zero elements for sparse arrays
We get the name and the global flag from the object, and reset
them to defaults after we've used them
'''
# get name and is_global from one-shot object store
name = self._var_name
is_global = self._var_is_global
# initialize the top-level matrix tag, store position
self._mat_tag_pos = self.file_stream.tell()
self.write_bytes(self.mat_tag)
# write array flags (complex, global, logical, class, nzmax)
af = np.zeros((), NDT_ARRAY_FLAGS)
af['data_type'] = miUINT32
af['byte_count'] = 8
flags = is_complex << 3 | is_global << 2 | is_logical << 1
af['flags_class'] = mclass | flags << 8
af['nzmax'] = nzmax
self.write_bytes(af)
# shape
self.write_element(np.array(shape, dtype='i4'))
# write name
name = np.asarray(name)
if name == '': # empty string zero-terminated
self.write_smalldata_element(name, miINT8, 0)
else:
self.write_element(name, miINT8)
# reset the one-shot store to defaults
self._var_name = ''
self._var_is_global = False
def update_matrix_tag(self, start_pos):
curr_pos = self.file_stream.tell()
self.file_stream.seek(start_pos)
byte_count = curr_pos - start_pos - 8
if byte_count >= 2**32:
raise MatWriteError("Matrix too large to save with Matlab "
"5 format")
self.mat_tag['byte_count'] = byte_count
self.write_bytes(self.mat_tag)
self.file_stream.seek(curr_pos)
def write_top(self, arr, name, is_global):
""" Write variable at top level of mat file
Parameters
----------
arr : array_like
array-like object to create writer for
name : str, optional
name as it will appear in matlab workspace
default is empty string
is_global : {False, True}, optional
whether variable will be global on load into matlab
"""
# these are set before the top-level header write, and unset at
# the end of the same write, because they do not apply for lower levels
self._var_is_global = is_global
self._var_name = name
# write the header and data
self.write(arr)
def write(self, arr):
''' Write `arr` to stream at top and sub levels
Parameters
----------
arr : array_like
array-like object to create writer for
'''
# store position, so we can update the matrix tag
mat_tag_pos = self.file_stream.tell()
# First check if these are sparse
if scipy.sparse.issparse(arr):
self.write_sparse(arr)
self.update_matrix_tag(mat_tag_pos)
return
# Try to convert things that aren't arrays
narr = to_writeable(arr)
if narr is None:
raise TypeError('Could not convert %s (type %s) to array'
% (arr, type(arr)))
if isinstance(narr, MatlabObject):
self.write_object(narr)
elif isinstance(narr, MatlabFunction):
raise MatWriteError('Cannot write matlab functions')
elif narr is EmptyStructMarker: # empty struct array
self.write_empty_struct()
elif narr.dtype.fields: # struct array
self.write_struct(narr)
elif narr.dtype.hasobject: # cell array
self.write_cells(narr)
elif narr.dtype.kind in ('U', 'S'):
if self.unicode_strings:
codec = 'UTF8'
else:
codec = 'ascii'
self.write_char(narr, codec)
else:
self.write_numeric(narr)
self.update_matrix_tag(mat_tag_pos)
def write_numeric(self, arr):
imagf = arr.dtype.kind == 'c'
logif = arr.dtype.kind == 'b'
try:
mclass = NP_TO_MXTYPES[arr.dtype.str[1:]]
except KeyError:
# No matching matlab type, probably complex256 / float128 / float96
# Cast data to complex128 / float64.
if imagf:
arr = arr.astype('c128')
elif logif:
arr = arr.astype('i1') # Should only contain 0/1
else:
arr = arr.astype('f8')
mclass = mxDOUBLE_CLASS
self.write_header(matdims(arr, self.oned_as),
mclass,
is_complex=imagf,
is_logical=logif)
if imagf:
self.write_element(arr.real)
self.write_element(arr.imag)
else:
self.write_element(arr)
def write_char(self, arr, codec='ascii'):
''' Write string array `arr` with given `codec`
'''
if arr.size == 0 or np.all(arr == ''):
# This an empty string array or a string array containing
# only empty strings. Matlab cannot distiguish between a
# string array that is empty, and a string array containing
# only empty strings, because it stores strings as arrays of
# char. There is no way of having an array of char that is
# not empty, but contains an empty string. We have to
# special-case the array-with-empty-strings because even
# empty strings have zero padding, which would otherwise
# appear in matlab as a string with a space.
shape = (0,) * np.max([arr.ndim, 2])
self.write_header(shape, mxCHAR_CLASS)
self.write_smalldata_element(arr, miUTF8, 0)
return
# non-empty string.
#
# Convert to char array
arr = arr_to_chars(arr)
# We have to write the shape directly, because we are going
# recode the characters, and the resulting stream of chars
# may have a different length
shape = arr.shape
self.write_header(shape, mxCHAR_CLASS)
if arr.dtype.kind == 'U' and arr.size:
# Make one long string from all the characters. We need to
# transpose here, because we're flattening the array, before
# we write the bytes. The bytes have to be written in
# Fortran order.
n_chars = np.product(shape)
st_arr = np.ndarray(shape=(),
dtype=arr_dtype_number(arr, n_chars),
buffer=arr.T.copy()) # Fortran order
# Recode with codec to give byte string
st = st_arr.item().encode(codec)
# Reconstruct as one-dimensional byte array
arr = np.ndarray(shape=(len(st),),
dtype='S1',
buffer=st)
self.write_element(arr, mdtype=miUTF8)
def write_sparse(self, arr):
''' Sparse matrices are 2D
'''
A = arr.tocsc() # convert to sparse CSC format
A.sort_indices() # MATLAB expects sorted row indices
is_complex = (A.dtype.kind == 'c')
is_logical = (A.dtype.kind == 'b')
nz = A.nnz
self.write_header(matdims(arr, self.oned_as),
mxSPARSE_CLASS,
is_complex=is_complex,
is_logical=is_logical,
# matlab won't load file with 0 nzmax
nzmax=1 if nz == 0 else nz)
self.write_element(A.indices.astype('i4'))
self.write_element(A.indptr.astype('i4'))
self.write_element(A.data.real)
if is_complex:
self.write_element(A.data.imag)
def write_cells(self, arr):
self.write_header(matdims(arr, self.oned_as),
mxCELL_CLASS)
# loop over data, column major
A = np.atleast_2d(arr).flatten('F')
for el in A:
self.write(el)
def write_empty_struct(self):
self.write_header((1, 1), mxSTRUCT_CLASS)
# max field name length set to 1 in an example matlab struct
self.write_element(np.array(1, dtype=np.int32))
# Field names element is empty
self.write_element(np.array([], dtype=np.int8))
def write_struct(self, arr):
self.write_header(matdims(arr, self.oned_as),
mxSTRUCT_CLASS)
self._write_items(arr)
def _write_items(self, arr):
# write fieldnames
fieldnames = [f[0] for f in arr.dtype.descr]
length = max([len(fieldname) for fieldname in fieldnames])+1
max_length = (self.long_field_names and 64) or 32
if length > max_length:
raise ValueError("Field names are restricted to %d characters" %
(max_length-1))
self.write_element(np.array([length], dtype='i4'))
self.write_element(
np.array(fieldnames, dtype='S%d' % (length)),
mdtype=miINT8)
A = np.atleast_2d(arr).flatten('F')
for el in A:
for f in fieldnames:
self.write(el[f])
def write_object(self, arr):
'''Same as writing structs, except different mx class, and extra
classname element after header
'''
self.write_header(matdims(arr, self.oned_as),
mxOBJECT_CLASS)
self.write_element(np.array(arr.classname, dtype='S'),
mdtype=miINT8)
self._write_items(arr)
class MatFile5Writer(object):
''' Class for writing mat5 files '''
@docfiller
def __init__(self, file_stream,
do_compression=False,
unicode_strings=False,
global_vars=None,
long_field_names=False,
oned_as='row'):
''' Initialize writer for matlab 5 format files
Parameters
----------
%(do_compression)s
%(unicode_strings)s
global_vars : None or sequence of strings, optional
Names of variables to be marked as global for matlab
%(long_fields)s
%(oned_as)s
'''
self.file_stream = file_stream
self.do_compression = do_compression
self.unicode_strings = unicode_strings
if global_vars:
self.global_vars = global_vars
else:
self.global_vars = []
self.long_field_names = long_field_names
self.oned_as = oned_as
self._matrix_writer = None
def write_file_header(self):
# write header
hdr = np.zeros((), NDT_FILE_HDR)
hdr['description'] = 'MATLAB 5.0 MAT-file Platform: %s, Created on: %s' \
% (os.name,time.asctime())
hdr['version'] = 0x0100
hdr['endian_test'] = np.ndarray(shape=(),
dtype='S2',
buffer=np.uint16(0x4d49))
self.file_stream.write(hdr.tostring())
def put_variables(self, mdict, write_header=None):
''' Write variables in `mdict` to stream
Parameters
----------
mdict : mapping
mapping with method ``items`` returns name, contents pairs where
``name`` which will appear in the matlab workspace in file load, and
``contents`` is something writeable to a matlab file, such as a numpy
array.
write_header : {None, True, False}, optional
If True, then write the matlab file header before writing the
variables. If None (the default) then write the file header
if we are at position 0 in the stream. By setting False
here, and setting the stream position to the end of the file,
you can append variables to a matlab file
'''
# write header if requested, or None and start of file
if write_header is None:
write_header = self.file_stream.tell() == 0
if write_header:
self.write_file_header()
self._matrix_writer = VarWriter5(self)
for name, var in mdict.items():
if name[0] == '_':
continue
is_global = name in self.global_vars
if self.do_compression:
stream = BytesIO()
self._matrix_writer.file_stream = stream
self._matrix_writer.write_top(var, asbytes(name), is_global)
out_str = zlib.compress(stream.getvalue())
tag = np.empty((), NDT_TAG_FULL)
tag['mdtype'] = miCOMPRESSED
tag['byte_count'] = len(out_str)
self.file_stream.write(tag.tostring())
self.file_stream.write(out_str)
else: # not compressing
self._matrix_writer.write_top(var, asbytes(name), is_global)
| 31,895 | 36.524706 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/setup.py
|
from __future__ import division, print_function, absolute_import
def configuration(parent_package='io',top_path=None):
from numpy.distutils.misc_util import Configuration
config = Configuration('matlab', parent_package, top_path)
config.add_extension('streams', sources=['streams.c'])
config.add_extension('mio_utils', sources=['mio_utils.c'])
config.add_extension('mio5_utils', sources=['mio5_utils.c'])
config.add_data_dir('tests')
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())
| 599 | 34.294118 | 64 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/mio5_params.py
|
''' Constants and classes for matlab 5 read and write
See also mio5_utils.pyx where these same constants arise as c enums.
If you make changes in this file, don't forget to change mio5_utils.pyx
'''
from __future__ import division, print_function, absolute_import
import numpy as np
from .miobase import convert_dtypes
miINT8 = 1
miUINT8 = 2
miINT16 = 3
miUINT16 = 4
miINT32 = 5
miUINT32 = 6
miSINGLE = 7
miDOUBLE = 9
miINT64 = 12
miUINT64 = 13
miMATRIX = 14
miCOMPRESSED = 15
miUTF8 = 16
miUTF16 = 17
miUTF32 = 18
mxCELL_CLASS = 1
mxSTRUCT_CLASS = 2
# The March 2008 edition of "Matlab 7 MAT-File Format" says that
# mxOBJECT_CLASS = 3, whereas matrix.h says that mxLOGICAL = 3.
# Matlab 2008a appears to save logicals as type 9, so we assume that
# the document is correct. See type 18, below.
mxOBJECT_CLASS = 3
mxCHAR_CLASS = 4
mxSPARSE_CLASS = 5
mxDOUBLE_CLASS = 6
mxSINGLE_CLASS = 7
mxINT8_CLASS = 8
mxUINT8_CLASS = 9
mxINT16_CLASS = 10
mxUINT16_CLASS = 11
mxINT32_CLASS = 12
mxUINT32_CLASS = 13
# The following are not in the March 2008 edition of "Matlab 7
# MAT-File Format," but were guessed from matrix.h.
mxINT64_CLASS = 14
mxUINT64_CLASS = 15
mxFUNCTION_CLASS = 16
# Not doing anything with these at the moment.
mxOPAQUE_CLASS = 17 # This appears to be a function workspace
# Thread 'saveing/loading symbol table of annymous functions', octave-maintainers, April-May 2007
# https://lists.gnu.org/archive/html/octave-maintainers/2007-04/msg00031.html
# https://lists.gnu.org/archive/html/octave-maintainers/2007-05/msg00032.html
# (Was/Deprecated: https://www-old.cae.wisc.edu/pipermail/octave-maintainers/2007-May/002824.html)
mxOBJECT_CLASS_FROM_MATRIX_H = 18
mdtypes_template = {
miINT8: 'i1',
miUINT8: 'u1',
miINT16: 'i2',
miUINT16: 'u2',
miINT32: 'i4',
miUINT32: 'u4',
miSINGLE: 'f4',
miDOUBLE: 'f8',
miINT64: 'i8',
miUINT64: 'u8',
miUTF8: 'u1',
miUTF16: 'u2',
miUTF32: 'u4',
'file_header': [('description', 'S116'),
('subsystem_offset', 'i8'),
('version', 'u2'),
('endian_test', 'S2')],
'tag_full': [('mdtype', 'u4'), ('byte_count', 'u4')],
'tag_smalldata':[('byte_count_mdtype', 'u4'), ('data', 'S4')],
'array_flags': [('data_type', 'u4'),
('byte_count', 'u4'),
('flags_class','u4'),
('nzmax', 'u4')],
'U1': 'U1',
}
mclass_dtypes_template = {
mxINT8_CLASS: 'i1',
mxUINT8_CLASS: 'u1',
mxINT16_CLASS: 'i2',
mxUINT16_CLASS: 'u2',
mxINT32_CLASS: 'i4',
mxUINT32_CLASS: 'u4',
mxINT64_CLASS: 'i8',
mxUINT64_CLASS: 'u8',
mxSINGLE_CLASS: 'f4',
mxDOUBLE_CLASS: 'f8',
}
mclass_info = {
mxINT8_CLASS: 'int8',
mxUINT8_CLASS: 'uint8',
mxINT16_CLASS: 'int16',
mxUINT16_CLASS: 'uint16',
mxINT32_CLASS: 'int32',
mxUINT32_CLASS: 'uint32',
mxINT64_CLASS: 'int64',
mxUINT64_CLASS: 'uint64',
mxSINGLE_CLASS: 'single',
mxDOUBLE_CLASS: 'double',
mxCELL_CLASS: 'cell',
mxSTRUCT_CLASS: 'struct',
mxOBJECT_CLASS: 'object',
mxCHAR_CLASS: 'char',
mxSPARSE_CLASS: 'sparse',
mxFUNCTION_CLASS: 'function',
mxOPAQUE_CLASS: 'opaque',
}
NP_TO_MTYPES = {
'f8': miDOUBLE,
'c32': miDOUBLE,
'c24': miDOUBLE,
'c16': miDOUBLE,
'f4': miSINGLE,
'c8': miSINGLE,
'i8': miINT64,
'i4': miINT32,
'i2': miINT16,
'i1': miINT8,
'u8': miUINT64,
'u4': miUINT32,
'u2': miUINT16,
'u1': miUINT8,
'S1': miUINT8,
'U1': miUTF16,
'b1': miUINT8, # not standard but seems MATLAB uses this (gh-4022)
}
NP_TO_MXTYPES = {
'f8': mxDOUBLE_CLASS,
'c32': mxDOUBLE_CLASS,
'c24': mxDOUBLE_CLASS,
'c16': mxDOUBLE_CLASS,
'f4': mxSINGLE_CLASS,
'c8': mxSINGLE_CLASS,
'i8': mxINT64_CLASS,
'i4': mxINT32_CLASS,
'i2': mxINT16_CLASS,
'i1': mxINT8_CLASS,
'u8': mxUINT64_CLASS,
'u4': mxUINT32_CLASS,
'u2': mxUINT16_CLASS,
'u1': mxUINT8_CLASS,
'S1': mxUINT8_CLASS,
'b1': mxUINT8_CLASS, # not standard but seems MATLAB uses this
}
''' Before release v7.1 (release 14) matlab (TM) used the system
default character encoding scheme padded out to 16-bits. Release 14
and later use Unicode. When saving character data, R14 checks if it
can be encoded in 7-bit ascii, and saves in that format if so.'''
codecs_template = {
miUTF8: {'codec': 'utf_8', 'width': 1},
miUTF16: {'codec': 'utf_16', 'width': 2},
miUTF32: {'codec': 'utf_32','width': 4},
}
def _convert_codecs(template, byte_order):
''' Convert codec template mapping to byte order
Set codecs not on this system to None
Parameters
----------
template : mapping
key, value are respectively codec name, and root name for codec
(without byte order suffix)
byte_order : {'<', '>'}
code for little or big endian
Returns
-------
codecs : dict
key, value are name, codec (as in .encode(codec))
'''
codecs = {}
postfix = byte_order == '<' and '_le' or '_be'
for k, v in template.items():
codec = v['codec']
try:
" ".encode(codec)
except LookupError:
codecs[k] = None
continue
if v['width'] > 1:
codec += postfix
codecs[k] = codec
return codecs.copy()
MDTYPES = {}
for _bytecode in '<>':
_def = {'dtypes': convert_dtypes(mdtypes_template, _bytecode),
'classes': convert_dtypes(mclass_dtypes_template, _bytecode),
'codecs': _convert_codecs(codecs_template, _bytecode)}
MDTYPES[_bytecode] = _def
class mat_struct(object):
''' Placeholder for holding read data from structs
We use instances of this class when the user passes False as a value to the
``struct_as_record`` parameter of the :func:`scipy.io.matlab.loadmat`
function.
'''
pass
class MatlabObject(np.ndarray):
''' ndarray Subclass to contain matlab object '''
def __new__(cls, input_array, classname=None):
# Input array is an already formed ndarray instance
# We first cast to be our class type
obj = np.asarray(input_array).view(cls)
# add the new attribute to the created instance
obj.classname = classname
# Finally, we must return the newly created object:
return obj
def __array_finalize__(self,obj):
# reset the attribute from passed original object
self.classname = getattr(obj, 'classname', None)
# We do not need to return anything
class MatlabFunction(np.ndarray):
''' Subclass to signal this is a matlab function '''
def __new__(cls, input_array):
obj = np.asarray(input_array).view(cls)
return obj
class MatlabOpaque(np.ndarray):
''' Subclass to signal this is a matlab opaque matrix '''
def __new__(cls, input_array):
obj = np.asarray(input_array).view(cls)
return obj
OPAQUE_DTYPE = np.dtype(
[('s0', 'O'), ('s1', 'O'), ('s2', 'O'), ('arr', 'O')])
| 7,079 | 26.764706 | 98 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/mio.py
|
"""
Module for reading and writing matlab (TM) .mat files
"""
# Authors: Travis Oliphant, Matthew Brett
from __future__ import division, print_function, absolute_import
import numpy as np
from scipy._lib.six import string_types
from .miobase import get_matfile_version, docfiller
from .mio4 import MatFile4Reader, MatFile4Writer
from .mio5 import MatFile5Reader, MatFile5Writer
__all__ = ['mat_reader_factory', 'loadmat', 'savemat', 'whosmat']
def _open_file(file_like, appendmat):
"""
Open `file_like` and return as file-like object. First, check if object is
already file-like; if so, return it as-is. Otherwise, try to pass it
to open(). If that fails, and `file_like` is a string, and `appendmat` is true,
append '.mat' and try again.
"""
try:
file_like.read(0)
return file_like, False
except AttributeError:
pass
try:
return open(file_like, 'rb'), True
except IOError:
# Probably "not found"
if isinstance(file_like, string_types):
if appendmat and not file_like.endswith('.mat'):
file_like += '.mat'
return open(file_like, 'rb'), True
else:
raise IOError('Reader needs file name or open file-like object')
@docfiller
def mat_reader_factory(file_name, appendmat=True, **kwargs):
"""
Create reader for matlab .mat format files.
Parameters
----------
%(file_arg)s
%(append_arg)s
%(load_args)s
%(struct_arg)s
Returns
-------
matreader : MatFileReader object
Initialized instance of MatFileReader class matching the mat file
type detected in `filename`.
file_opened : bool
Whether the file was opened by this routine.
"""
byte_stream, file_opened = _open_file(file_name, appendmat)
mjv, mnv = get_matfile_version(byte_stream)
if mjv == 0:
return MatFile4Reader(byte_stream, **kwargs), file_opened
elif mjv == 1:
return MatFile5Reader(byte_stream, **kwargs), file_opened
elif mjv == 2:
raise NotImplementedError('Please use HDF reader for matlab v7.3 files')
else:
raise TypeError('Did not recognize version %s' % mjv)
@docfiller
def loadmat(file_name, mdict=None, appendmat=True, **kwargs):
"""
Load MATLAB file.
Parameters
----------
file_name : str
Name of the mat file (do not need .mat extension if
appendmat==True). Can also pass open file-like object.
mdict : dict, optional
Dictionary in which to insert matfile variables.
appendmat : bool, optional
True to append the .mat extension to the end of the given
filename, if not already present.
byte_order : str or None, optional
None by default, implying byte order guessed from mat
file. Otherwise can be one of ('native', '=', 'little', '<',
'BIG', '>').
mat_dtype : bool, optional
If True, return arrays in same dtype as would be loaded into
MATLAB (instead of the dtype with which they are saved).
squeeze_me : bool, optional
Whether to squeeze unit matrix dimensions or not.
chars_as_strings : bool, optional
Whether to convert char arrays to string arrays.
matlab_compatible : bool, optional
Returns matrices as would be loaded by MATLAB (implies
squeeze_me=False, chars_as_strings=False, mat_dtype=True,
struct_as_record=True).
struct_as_record : bool, optional
Whether to load MATLAB structs as numpy record arrays, or as
old-style numpy arrays with dtype=object. Setting this flag to
False replicates the behavior of scipy version 0.7.x (returning
numpy object arrays). The default setting is True, because it
allows easier round-trip load and save of MATLAB files.
verify_compressed_data_integrity : bool, optional
Whether the length of compressed sequences in the MATLAB file
should be checked, to ensure that they are not longer than we expect.
It is advisable to enable this (the default) because overlong
compressed sequences in MATLAB files generally indicate that the
files have experienced some sort of corruption.
variable_names : None or sequence
If None (the default) - read all variables in file. Otherwise
`variable_names` should be a sequence of strings, giving names of the
matlab variables to read from the file. The reader will skip any
variable with a name not in this sequence, possibly saving some read
processing.
Returns
-------
mat_dict : dict
dictionary with variable names as keys, and loaded matrices as
values.
Notes
-----
v4 (Level 1.0), v6 and v7 to 7.2 matfiles are supported.
You will need an HDF5 python library to read matlab 7.3 format mat
files. Because scipy does not supply one, we do not implement the
HDF5 / 7.3 interface here.
"""
variable_names = kwargs.pop('variable_names', None)
MR, file_opened = mat_reader_factory(file_name, appendmat, **kwargs)
matfile_dict = MR.get_variables(variable_names)
if mdict is not None:
mdict.update(matfile_dict)
else:
mdict = matfile_dict
if file_opened:
MR.mat_stream.close()
return mdict
@docfiller
def savemat(file_name, mdict,
appendmat=True,
format='5',
long_field_names=False,
do_compression=False,
oned_as='row'):
"""
Save a dictionary of names and arrays into a MATLAB-style .mat file.
This saves the array objects in the given dictionary to a MATLAB-
style .mat file.
Parameters
----------
file_name : str or file-like object
Name of the .mat file (.mat extension not needed if ``appendmat ==
True``).
Can also pass open file_like object.
mdict : dict
Dictionary from which to save matfile variables.
appendmat : bool, optional
True (the default) to append the .mat extension to the end of the
given filename, if not already present.
format : {'5', '4'}, string, optional
'5' (the default) for MATLAB 5 and up (to 7.2),
'4' for MATLAB 4 .mat files.
long_field_names : bool, optional
False (the default) - maximum field name length in a structure is
31 characters which is the documented maximum length.
True - maximum field name length in a structure is 63 characters
which works for MATLAB 7.6+.
do_compression : bool, optional
Whether or not to compress matrices on write. Default is False.
oned_as : {'row', 'column'}, optional
If 'column', write 1-D numpy arrays as column vectors.
If 'row', write 1-D numpy arrays as row vectors.
See also
--------
mio4.MatFile4Writer
mio5.MatFile5Writer
"""
file_opened = False
if hasattr(file_name, 'write'):
# File-like object already; use as-is
file_stream = file_name
else:
if isinstance(file_name, string_types):
if appendmat and not file_name.endswith('.mat'):
file_name = file_name + ".mat"
file_stream = open(file_name, 'wb')
file_opened = True
if format == '4':
if long_field_names:
raise ValueError("Long field names are not available for version 4 files")
MW = MatFile4Writer(file_stream, oned_as)
elif format == '5':
MW = MatFile5Writer(file_stream,
do_compression=do_compression,
unicode_strings=True,
long_field_names=long_field_names,
oned_as=oned_as)
else:
raise ValueError("Format should be '4' or '5'")
MW.put_variables(mdict)
if file_opened:
file_stream.close()
@docfiller
def whosmat(file_name, appendmat=True, **kwargs):
"""
List variables inside a MATLAB file.
Parameters
----------
%(file_arg)s
%(append_arg)s
%(load_args)s
%(struct_arg)s
Returns
-------
variables : list of tuples
A list of tuples, where each tuple holds the matrix name (a string),
its shape (tuple of ints), and its data class (a string).
Possible data classes are: int8, uint8, int16, uint16, int32, uint32,
int64, uint64, single, double, cell, struct, object, char, sparse,
function, opaque, logical, unknown.
Notes
-----
v4 (Level 1.0), v6 and v7 to 7.2 matfiles are supported.
You will need an HDF5 python library to read matlab 7.3 format mat
files. Because scipy does not supply one, we do not implement the
HDF5 / 7.3 interface here.
.. versionadded:: 0.12.0
"""
ML, file_opened = mat_reader_factory(file_name, **kwargs)
variables = ML.list_variables()
if file_opened:
ML.mat_stream.close()
return variables
| 8,958 | 33.32567 | 86 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/mio4.py
|
''' Classes for read / write of matlab (TM) 4 files
'''
from __future__ import division, print_function, absolute_import
import sys
import warnings
import numpy as np
from numpy.compat import asbytes, asstr
import scipy.sparse
from scipy._lib.six import string_types
from .miobase import (MatFileReader, docfiller, matdims, read_dtype,
convert_dtypes, arr_to_chars, arr_dtype_number)
from .mio_utils import squeeze_element, chars_to_strings
from functools import reduce
SYS_LITTLE_ENDIAN = sys.byteorder == 'little'
miDOUBLE = 0
miSINGLE = 1
miINT32 = 2
miINT16 = 3
miUINT16 = 4
miUINT8 = 5
mdtypes_template = {
miDOUBLE: 'f8',
miSINGLE: 'f4',
miINT32: 'i4',
miINT16: 'i2',
miUINT16: 'u2',
miUINT8: 'u1',
'header': [('mopt', 'i4'),
('mrows', 'i4'),
('ncols', 'i4'),
('imagf', 'i4'),
('namlen', 'i4')],
'U1': 'U1',
}
np_to_mtypes = {
'f8': miDOUBLE,
'c32': miDOUBLE,
'c24': miDOUBLE,
'c16': miDOUBLE,
'f4': miSINGLE,
'c8': miSINGLE,
'i4': miINT32,
'i2': miINT16,
'u2': miUINT16,
'u1': miUINT8,
'S1': miUINT8,
}
# matrix classes
mxFULL_CLASS = 0
mxCHAR_CLASS = 1
mxSPARSE_CLASS = 2
order_codes = {
0: '<',
1: '>',
2: 'VAX D-float', # !
3: 'VAX G-float',
4: 'Cray', # !!
}
mclass_info = {
mxFULL_CLASS: 'double',
mxCHAR_CLASS: 'char',
mxSPARSE_CLASS: 'sparse',
}
class VarHeader4(object):
# Mat4 variables never logical or global
is_logical = False
is_global = False
def __init__(self,
name,
dtype,
mclass,
dims,
is_complex):
self.name = name
self.dtype = dtype
self.mclass = mclass
self.dims = dims
self.is_complex = is_complex
class VarReader4(object):
''' Class to read matlab 4 variables '''
def __init__(self, file_reader):
self.file_reader = file_reader
self.mat_stream = file_reader.mat_stream
self.dtypes = file_reader.dtypes
self.chars_as_strings = file_reader.chars_as_strings
self.squeeze_me = file_reader.squeeze_me
def read_header(self):
''' Read and return header for variable '''
data = read_dtype(self.mat_stream, self.dtypes['header'])
name = self.mat_stream.read(int(data['namlen'])).strip(b'\x00')
if data['mopt'] < 0 or data['mopt'] > 5000:
raise ValueError('Mat 4 mopt wrong format, byteswapping problem?')
M, rest = divmod(data['mopt'], 1000) # order code
if M not in (0, 1):
warnings.warn("We do not support byte ordering '%s'; returned "
"data may be corrupt" % order_codes[M],
UserWarning)
O, rest = divmod(rest, 100) # unused, should be 0
if O != 0:
raise ValueError('O in MOPT integer should be 0, wrong format?')
P, rest = divmod(rest, 10) # data type code e.g miDOUBLE (see above)
T = rest # matrix type code e.g. mxFULL_CLASS (see above)
dims = (data['mrows'], data['ncols'])
is_complex = data['imagf'] == 1
dtype = self.dtypes[P]
return VarHeader4(
name,
dtype,
T,
dims,
is_complex)
def array_from_header(self, hdr, process=True):
mclass = hdr.mclass
if mclass == mxFULL_CLASS:
arr = self.read_full_array(hdr)
elif mclass == mxCHAR_CLASS:
arr = self.read_char_array(hdr)
if process and self.chars_as_strings:
arr = chars_to_strings(arr)
elif mclass == mxSPARSE_CLASS:
# no current processing (below) makes sense for sparse
return self.read_sparse_array(hdr)
else:
raise TypeError('No reader for class code %s' % mclass)
if process and self.squeeze_me:
return squeeze_element(arr)
return arr
def read_sub_array(self, hdr, copy=True):
''' Mat4 read using header `hdr` dtype and dims
Parameters
----------
hdr : object
object with attributes ``dtype``, ``dims``. dtype is assumed to be
the correct endianness
copy : bool, optional
copies array before return if True (default True)
(buffer is usually read only)
Returns
-------
arr : ndarray
of dtype givem by `hdr` ``dtype`` and shape givem by `hdr` ``dims``
'''
dt = hdr.dtype
dims = hdr.dims
num_bytes = dt.itemsize
for d in dims:
num_bytes *= d
buffer = self.mat_stream.read(int(num_bytes))
if len(buffer) != num_bytes:
raise ValueError("Not enough bytes to read matrix '%s'; is this "
"a badly-formed file? Consider listing matrices "
"with `whosmat` and loading named matrices with "
"`variable_names` kwarg to `loadmat`" % hdr.name)
arr = np.ndarray(shape=dims,
dtype=dt,
buffer=buffer,
order='F')
if copy:
arr = arr.copy()
return arr
def read_full_array(self, hdr):
''' Full (rather than sparse) matrix getter
Read matrix (array) can be real or complex
Parameters
----------
hdr : ``VarHeader4`` instance
Returns
-------
arr : ndarray
complex array if ``hdr.is_complex`` is True, otherwise a real
numeric array
'''
if hdr.is_complex:
# avoid array copy to save memory
res = self.read_sub_array(hdr, copy=False)
res_j = self.read_sub_array(hdr, copy=False)
return res + (res_j * 1j)
return self.read_sub_array(hdr)
def read_char_array(self, hdr):
''' latin-1 text matrix (char matrix) reader
Parameters
----------
hdr : ``VarHeader4`` instance
Returns
-------
arr : ndarray
with dtype 'U1', shape given by `hdr` ``dims``
'''
arr = self.read_sub_array(hdr).astype(np.uint8)
S = arr.tostring().decode('latin-1')
return np.ndarray(shape=hdr.dims,
dtype=np.dtype('U1'),
buffer=np.array(S)).copy()
def read_sparse_array(self, hdr):
''' Read and return sparse matrix type
Parameters
----------
hdr : ``VarHeader4`` instance
Returns
-------
arr : ``scipy.sparse.coo_matrix``
with dtype ``float`` and shape read from the sparse matrix data
Notes
-----
MATLAB 4 real sparse arrays are saved in a N+1 by 3 array format, where
N is the number of non-zero values. Column 1 values [0:N] are the
(1-based) row indices of the each non-zero value, column 2 [0:N] are the
column indices, column 3 [0:N] are the (real) values. The last values
[-1,0:2] of the rows, column indices are shape[0] and shape[1]
respectively of the output matrix. The last value for the values column
is a padding 0. mrows and ncols values from the header give the shape of
the stored matrix, here [N+1, 3]. Complex data is saved as a 4 column
matrix, where the fourth column contains the imaginary component; the
last value is again 0. Complex sparse data do *not* have the header
``imagf`` field set to True; the fact that the data are complex is only
detectable because there are 4 storage columns
'''
res = self.read_sub_array(hdr)
tmp = res[:-1,:]
# All numbers are float64 in Matlab, but Scipy sparse expects int shape
dims = (int(res[-1,0]), int(res[-1,1]))
I = np.ascontiguousarray(tmp[:,0],dtype='intc') # fixes byte order also
J = np.ascontiguousarray(tmp[:,1],dtype='intc')
I -= 1 # for 1-based indexing
J -= 1
if res.shape[1] == 3:
V = np.ascontiguousarray(tmp[:,2],dtype='float')
else:
V = np.ascontiguousarray(tmp[:,2],dtype='complex')
V.imag = tmp[:,3]
return scipy.sparse.coo_matrix((V,(I,J)), dims)
def shape_from_header(self, hdr):
'''Read the shape of the array described by the header.
The file position after this call is unspecified.
'''
mclass = hdr.mclass
if mclass == mxFULL_CLASS:
shape = tuple(map(int, hdr.dims))
elif mclass == mxCHAR_CLASS:
shape = tuple(map(int, hdr.dims))
if self.chars_as_strings:
shape = shape[:-1]
elif mclass == mxSPARSE_CLASS:
dt = hdr.dtype
dims = hdr.dims
if not (len(dims) == 2 and dims[0] >= 1 and dims[1] >= 1):
return ()
# Read only the row and column counts
self.mat_stream.seek(dt.itemsize * (dims[0] - 1), 1)
rows = np.ndarray(shape=(1,), dtype=dt,
buffer=self.mat_stream.read(dt.itemsize))
self.mat_stream.seek(dt.itemsize * (dims[0] - 1), 1)
cols = np.ndarray(shape=(1,), dtype=dt,
buffer=self.mat_stream.read(dt.itemsize))
shape = (int(rows), int(cols))
else:
raise TypeError('No reader for class code %s' % mclass)
if self.squeeze_me:
shape = tuple([x for x in shape if x != 1])
return shape
class MatFile4Reader(MatFileReader):
''' Reader for Mat4 files '''
@docfiller
def __init__(self, mat_stream, *args, **kwargs):
''' Initialize matlab 4 file reader
%(matstream_arg)s
%(load_args)s
'''
super(MatFile4Reader, self).__init__(mat_stream, *args, **kwargs)
self._matrix_reader = None
def guess_byte_order(self):
self.mat_stream.seek(0)
mopt = read_dtype(self.mat_stream, np.dtype('i4'))
self.mat_stream.seek(0)
if mopt == 0:
return '<'
if mopt < 0 or mopt > 5000:
# Number must have been byteswapped
return SYS_LITTLE_ENDIAN and '>' or '<'
# Not byteswapped
return SYS_LITTLE_ENDIAN and '<' or '>'
def initialize_read(self):
''' Run when beginning read of variables
Sets up readers from parameters in `self`
'''
self.dtypes = convert_dtypes(mdtypes_template, self.byte_order)
self._matrix_reader = VarReader4(self)
def read_var_header(self):
''' Read and return header, next position
Parameters
----------
None
Returns
-------
header : object
object that can be passed to self.read_var_array, and that
has attributes ``name`` and ``is_global``
next_position : int
position in stream of next variable
'''
hdr = self._matrix_reader.read_header()
n = reduce(lambda x, y: x*y, hdr.dims, 1) # fast product
remaining_bytes = hdr.dtype.itemsize * n
if hdr.is_complex and not hdr.mclass == mxSPARSE_CLASS:
remaining_bytes *= 2
next_position = self.mat_stream.tell() + remaining_bytes
return hdr, next_position
def read_var_array(self, header, process=True):
''' Read array, given `header`
Parameters
----------
header : header object
object with fields defining variable header
process : {True, False}, optional
If True, apply recursive post-processing during loading of array.
Returns
-------
arr : array
array with post-processing applied or not according to
`process`.
'''
return self._matrix_reader.array_from_header(header, process)
def get_variables(self, variable_names=None):
''' get variables from stream as dictionary
Parameters
----------
variable_names : None or str or sequence of str, optional
variable name, or sequence of variable names to get from Mat file /
file stream. If None, then get all variables in file
'''
if isinstance(variable_names, string_types):
variable_names = [variable_names]
elif variable_names is not None:
variable_names = list(variable_names)
self.mat_stream.seek(0)
# set up variable reader
self.initialize_read()
mdict = {}
while not self.end_of_stream():
hdr, next_position = self.read_var_header()
name = asstr(hdr.name)
if variable_names is not None and name not in variable_names:
self.mat_stream.seek(next_position)
continue
mdict[name] = self.read_var_array(hdr)
self.mat_stream.seek(next_position)
if variable_names is not None:
variable_names.remove(name)
if len(variable_names) == 0:
break
return mdict
def list_variables(self):
''' list variables from stream '''
self.mat_stream.seek(0)
# set up variable reader
self.initialize_read()
vars = []
while not self.end_of_stream():
hdr, next_position = self.read_var_header()
name = asstr(hdr.name)
shape = self._matrix_reader.shape_from_header(hdr)
info = mclass_info.get(hdr.mclass, 'unknown')
vars.append((name, shape, info))
self.mat_stream.seek(next_position)
return vars
def arr_to_2d(arr, oned_as='row'):
''' Make ``arr`` exactly two dimensional
If `arr` has more than 2 dimensions, raise a ValueError
Parameters
----------
arr : array
oned_as : {'row', 'column'}, optional
Whether to reshape 1D vectors as row vectors or column vectors.
See documentation for ``matdims`` for more detail
Returns
-------
arr2d : array
2D version of the array
'''
dims = matdims(arr, oned_as)
if len(dims) > 2:
raise ValueError('Matlab 4 files cannot save arrays with more than '
'2 dimensions')
return arr.reshape(dims)
class VarWriter4(object):
def __init__(self, file_writer):
self.file_stream = file_writer.file_stream
self.oned_as = file_writer.oned_as
def write_bytes(self, arr):
self.file_stream.write(arr.tostring(order='F'))
def write_string(self, s):
self.file_stream.write(s)
def write_header(self, name, shape, P=miDOUBLE, T=mxFULL_CLASS, imagf=0):
''' Write header for given data options
Parameters
----------
name : str
name of variable
shape : sequence
Shape of array as it will be read in matlab
P : int, optional
code for mat4 data type, one of ``miDOUBLE, miSINGLE, miINT32,
miINT16, miUINT16, miUINT8``
T : int, optional
code for mat4 matrix class, one of ``mxFULL_CLASS, mxCHAR_CLASS,
mxSPARSE_CLASS``
imagf : int, optional
flag indicating complex
'''
header = np.empty((), mdtypes_template['header'])
M = not SYS_LITTLE_ENDIAN
O = 0
header['mopt'] = (M * 1000 +
O * 100 +
P * 10 +
T)
header['mrows'] = shape[0]
header['ncols'] = shape[1]
header['imagf'] = imagf
header['namlen'] = len(name) + 1
self.write_bytes(header)
self.write_string(asbytes(name + '\0'))
def write(self, arr, name):
''' Write matrix `arr`, with name `name`
Parameters
----------
arr : array_like
array to write
name : str
name in matlab workspace
'''
# we need to catch sparse first, because np.asarray returns an
# an object array for scipy.sparse
if scipy.sparse.issparse(arr):
self.write_sparse(arr, name)
return
arr = np.asarray(arr)
dt = arr.dtype
if not dt.isnative:
arr = arr.astype(dt.newbyteorder('='))
dtt = dt.type
if dtt is np.object_:
raise TypeError('Cannot save object arrays in Mat4')
elif dtt is np.void:
raise TypeError('Cannot save void type arrays')
elif dtt in (np.unicode_, np.string_):
self.write_char(arr, name)
return
self.write_numeric(arr, name)
def write_numeric(self, arr, name):
arr = arr_to_2d(arr, self.oned_as)
imagf = arr.dtype.kind == 'c'
try:
P = np_to_mtypes[arr.dtype.str[1:]]
except KeyError:
if imagf:
arr = arr.astype('c128')
else:
arr = arr.astype('f8')
P = miDOUBLE
self.write_header(name,
arr.shape,
P=P,
T=mxFULL_CLASS,
imagf=imagf)
if imagf:
self.write_bytes(arr.real)
self.write_bytes(arr.imag)
else:
self.write_bytes(arr)
def write_char(self, arr, name):
arr = arr_to_chars(arr)
arr = arr_to_2d(arr, self.oned_as)
dims = arr.shape
self.write_header(
name,
dims,
P=miUINT8,
T=mxCHAR_CLASS)
if arr.dtype.kind == 'U':
# Recode unicode to latin1
n_chars = np.product(dims)
st_arr = np.ndarray(shape=(),
dtype=arr_dtype_number(arr, n_chars),
buffer=arr)
st = st_arr.item().encode('latin-1')
arr = np.ndarray(shape=dims, dtype='S1', buffer=st)
self.write_bytes(arr)
def write_sparse(self, arr, name):
''' Sparse matrices are 2D
See docstring for VarReader4.read_sparse_array
'''
A = arr.tocoo() # convert to sparse COO format (ijv)
imagf = A.dtype.kind == 'c'
ijv = np.zeros((A.nnz + 1, 3+imagf), dtype='f8')
ijv[:-1,0] = A.row
ijv[:-1,1] = A.col
ijv[:-1,0:2] += 1 # 1 based indexing
if imagf:
ijv[:-1,2] = A.data.real
ijv[:-1,3] = A.data.imag
else:
ijv[:-1,2] = A.data
ijv[-1,0:2] = A.shape
self.write_header(
name,
ijv.shape,
P=miDOUBLE,
T=mxSPARSE_CLASS)
self.write_bytes(ijv)
class MatFile4Writer(object):
''' Class for writing matlab 4 format files '''
def __init__(self, file_stream, oned_as=None):
self.file_stream = file_stream
if oned_as is None:
oned_as = 'row'
self.oned_as = oned_as
self._matrix_writer = None
def put_variables(self, mdict, write_header=None):
''' Write variables in `mdict` to stream
Parameters
----------
mdict : mapping
mapping with method ``items`` return name, contents pairs
where ``name`` which will appeak in the matlab workspace in
file load, and ``contents`` is something writeable to a
matlab file, such as a numpy array.
write_header : {None, True, False}
If True, then write the matlab file header before writing the
variables. If None (the default) then write the file header
if we are at position 0 in the stream. By setting False
here, and setting the stream position to the end of the file,
you can append variables to a matlab file
'''
# there is no header for a matlab 4 mat file, so we ignore the
# ``write_header`` input argument. It's there for compatibility
# with the matlab 5 version of this method
self._matrix_writer = VarWriter4(self)
for name, var in mdict.items():
self._matrix_writer.write(var, name)
| 20,384 | 31.932149 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/__init__.py
|
"""
Utilities for dealing with MATLAB(R) files
Notes
-----
MATLAB(R) is a registered trademark of The MathWorks, Inc., 3 Apple Hill
Drive, Natick, MA 01760-2098, USA.
"""
from __future__ import division, print_function, absolute_import
# Matlab file read and write utilities
from .mio import loadmat, savemat, whosmat
from . import byteordercodes
__all__ = ['loadmat', 'savemat', 'whosmat', 'byteordercodes']
from scipy._lib._testutils import PytestTester
test = PytestTester(__name__)
del PytestTester
| 508 | 23.238095 | 72 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/miobase.py
|
# Authors: Travis Oliphant, Matthew Brett
"""
Base classes for MATLAB file stream reading.
MATLAB is a registered trademark of the Mathworks inc.
"""
from __future__ import division, print_function, absolute_import
import sys
import operator
from scipy._lib.six import reduce
import numpy as np
if sys.version_info[0] >= 3:
byteord = int
else:
byteord = ord
from scipy.misc import doccer
from . import byteordercodes as boc
class MatReadError(Exception):
pass
class MatWriteError(Exception):
pass
class MatReadWarning(UserWarning):
pass
doc_dict = \
{'file_arg':
'''file_name : str
Name of the mat file (do not need .mat extension if
appendmat==True) Can also pass open file-like object.''',
'append_arg':
'''appendmat : bool, optional
True to append the .mat extension to the end of the given
filename, if not already present.''',
'load_args':
'''byte_order : str or None, optional
None by default, implying byte order guessed from mat
file. Otherwise can be one of ('native', '=', 'little', '<',
'BIG', '>').
mat_dtype : bool, optional
If True, return arrays in same dtype as would be loaded into
MATLAB (instead of the dtype with which they are saved).
squeeze_me : bool, optional
Whether to squeeze unit matrix dimensions or not.
chars_as_strings : bool, optional
Whether to convert char arrays to string arrays.
matlab_compatible : bool, optional
Returns matrices as would be loaded by MATLAB (implies
squeeze_me=False, chars_as_strings=False, mat_dtype=True,
struct_as_record=True).''',
'struct_arg':
'''struct_as_record : bool, optional
Whether to load MATLAB structs as numpy record arrays, or as
old-style numpy arrays with dtype=object. Setting this flag to
False replicates the behavior of scipy version 0.7.x (returning
numpy object arrays). The default setting is True, because it
allows easier round-trip load and save of MATLAB files.''',
'matstream_arg':
'''mat_stream : file-like
Object with file API, open for reading.''',
'long_fields':
'''long_field_names : bool, optional
* False - maximum field name length in a structure is 31 characters
which is the documented maximum length. This is the default.
* True - maximum field name length in a structure is 63 characters
which works for MATLAB 7.6''',
'do_compression':
'''do_compression : bool, optional
Whether to compress matrices on write. Default is False.''',
'oned_as':
'''oned_as : {'row', 'column'}, optional
If 'column', write 1-D numpy arrays as column vectors.
If 'row', write 1D numpy arrays as row vectors.''',
'unicode_strings':
'''unicode_strings : bool, optional
If True, write strings as Unicode, else MATLAB usual encoding.'''}
docfiller = doccer.filldoc(doc_dict)
'''
Note on architecture
======================
There are three sets of parameters relevant for reading files. The
first are *file read parameters* - containing options that are common
for reading the whole file, and therefore every variable within that
file. At the moment these are:
* mat_stream
* dtypes (derived from byte code)
* byte_order
* chars_as_strings
* squeeze_me
* struct_as_record (MATLAB 5 files)
* class_dtypes (derived from order code, MATLAB 5 files)
* codecs (MATLAB 5 files)
* uint16_codec (MATLAB 5 files)
Another set of parameters are those that apply only to the current
variable being read - the *header*:
* header related variables (different for v4 and v5 mat files)
* is_complex
* mclass
* var_stream
With the header, we need ``next_position`` to tell us where the next
variable in the stream is.
Then, for each element in a matrix, there can be *element read
parameters*. An element is, for example, one element in a MATLAB cell
array. At the moment these are:
* mat_dtype
The file-reading object contains the *file read parameters*. The
*header* is passed around as a data object, or may be read and discarded
in a single function. The *element read parameters* - the mat_dtype in
this instance, is passed into a general post-processing function - see
``mio_utils`` for details.
'''
def convert_dtypes(dtype_template, order_code):
''' Convert dtypes in mapping to given order
Parameters
----------
dtype_template : mapping
mapping with values returning numpy dtype from ``np.dtype(val)``
order_code : str
an order code suitable for using in ``dtype.newbyteorder()``
Returns
-------
dtypes : mapping
mapping where values have been replaced by
``np.dtype(val).newbyteorder(order_code)``
'''
dtypes = dtype_template.copy()
for k in dtypes:
dtypes[k] = np.dtype(dtypes[k]).newbyteorder(order_code)
return dtypes
def read_dtype(mat_stream, a_dtype):
"""
Generic get of byte stream data of known type
Parameters
----------
mat_stream : file_like object
MATLAB (tm) mat file stream
a_dtype : dtype
dtype of array to read. `a_dtype` is assumed to be correct
endianness.
Returns
-------
arr : ndarray
Array of dtype `a_dtype` read from stream.
"""
num_bytes = a_dtype.itemsize
arr = np.ndarray(shape=(),
dtype=a_dtype,
buffer=mat_stream.read(num_bytes),
order='F')
return arr
def get_matfile_version(fileobj):
"""
Return major, minor tuple depending on apparent mat file type
Where:
#. 0,x -> version 4 format mat files
#. 1,x -> version 5 format mat files
#. 2,x -> version 7.3 format mat files (HDF format)
Parameters
----------
fileobj : file_like
object implementing seek() and read()
Returns
-------
major_version : {0, 1, 2}
major MATLAB File format version
minor_version : int
minor MATLAB file format version
Raises
------
MatReadError
If the file is empty.
ValueError
The matfile version is unknown.
Notes
-----
Has the side effect of setting the file read pointer to 0
"""
# Mat4 files have a zero somewhere in first 4 bytes
fileobj.seek(0)
mopt_bytes = fileobj.read(4)
if len(mopt_bytes) == 0:
raise MatReadError("Mat file appears to be empty")
mopt_ints = np.ndarray(shape=(4,), dtype=np.uint8, buffer=mopt_bytes)
if 0 in mopt_ints:
fileobj.seek(0)
return (0,0)
# For 5 format or 7.3 format we need to read an integer in the
# header. Bytes 124 through 128 contain a version integer and an
# endian test string
fileobj.seek(124)
tst_str = fileobj.read(4)
fileobj.seek(0)
maj_ind = int(tst_str[2] == b'I'[0])
maj_val = byteord(tst_str[maj_ind])
min_val = byteord(tst_str[1-maj_ind])
ret = (maj_val, min_val)
if maj_val in (1, 2):
return ret
raise ValueError('Unknown mat file type, version %s, %s' % ret)
def matdims(arr, oned_as='column'):
"""
Determine equivalent MATLAB dimensions for given array
Parameters
----------
arr : ndarray
Input array
oned_as : {'column', 'row'}, optional
Whether 1-D arrays are returned as MATLAB row or column matrices.
Default is 'column'.
Returns
-------
dims : tuple
Shape tuple, in the form MATLAB expects it.
Notes
-----
We had to decide what shape a 1 dimensional array would be by
default. ``np.atleast_2d`` thinks it is a row vector. The
default for a vector in MATLAB (e.g. ``>> 1:12``) is a row vector.
Versions of scipy up to and including 0.11 resulted (accidentally)
in 1-D arrays being read as column vectors. For the moment, we
maintain the same tradition here.
Examples
--------
>>> matdims(np.array(1)) # numpy scalar
(1, 1)
>>> matdims(np.array([1])) # 1d array, 1 element
(1, 1)
>>> matdims(np.array([1,2])) # 1d array, 2 elements
(2, 1)
>>> matdims(np.array([[2],[3]])) # 2d array, column vector
(2, 1)
>>> matdims(np.array([[2,3]])) # 2d array, row vector
(1, 2)
>>> matdims(np.array([[[2,3]]])) # 3d array, rowish vector
(1, 1, 2)
>>> matdims(np.array([])) # empty 1d array
(0, 0)
>>> matdims(np.array([[]])) # empty 2d
(0, 0)
>>> matdims(np.array([[[]]])) # empty 3d
(0, 0, 0)
Optional argument flips 1-D shape behavior.
>>> matdims(np.array([1,2]), 'row') # 1d array, 2 elements
(1, 2)
The argument has to make sense though
>>> matdims(np.array([1,2]), 'bizarre')
Traceback (most recent call last):
...
ValueError: 1D option "bizarre" is strange
"""
shape = arr.shape
if shape == (): # scalar
return (1,1)
if reduce(operator.mul, shape) == 0: # zero elememts
return (0,) * np.max([arr.ndim, 2])
if len(shape) == 1: # 1D
if oned_as == 'column':
return shape + (1,)
elif oned_as == 'row':
return (1,) + shape
else:
raise ValueError('1D option "%s" is strange'
% oned_as)
return shape
class MatVarReader(object):
''' Abstract class defining required interface for var readers'''
def __init__(self, file_reader):
pass
def read_header(self):
''' Returns header '''
pass
def array_from_header(self, header):
''' Reads array given header '''
pass
class MatFileReader(object):
""" Base object for reading mat files
To make this class functional, you will need to override the
following methods:
matrix_getter_factory - gives object to fetch next matrix from stream
guess_byte_order - guesses file byte order from file
"""
@docfiller
def __init__(self, mat_stream,
byte_order=None,
mat_dtype=False,
squeeze_me=False,
chars_as_strings=True,
matlab_compatible=False,
struct_as_record=True,
verify_compressed_data_integrity=True
):
'''
Initializer for mat file reader
mat_stream : file-like
object with file API, open for reading
%(load_args)s
'''
# Initialize stream
self.mat_stream = mat_stream
self.dtypes = {}
if not byte_order:
byte_order = self.guess_byte_order()
else:
byte_order = boc.to_numpy_code(byte_order)
self.byte_order = byte_order
self.struct_as_record = struct_as_record
if matlab_compatible:
self.set_matlab_compatible()
else:
self.squeeze_me = squeeze_me
self.chars_as_strings = chars_as_strings
self.mat_dtype = mat_dtype
self.verify_compressed_data_integrity = verify_compressed_data_integrity
def set_matlab_compatible(self):
''' Sets options to return arrays as MATLAB loads them '''
self.mat_dtype = True
self.squeeze_me = False
self.chars_as_strings = False
def guess_byte_order(self):
''' As we do not know what file type we have, assume native '''
return boc.native_code
def end_of_stream(self):
b = self.mat_stream.read(1)
curpos = self.mat_stream.tell()
self.mat_stream.seek(curpos-1)
return len(b) == 0
def arr_dtype_number(arr, num):
''' Return dtype for given number of items per element'''
return np.dtype(arr.dtype.str[:2] + str(num))
def arr_to_chars(arr):
''' Convert string array to char array '''
dims = list(arr.shape)
if not dims:
dims = [1]
dims.append(int(arr.dtype.str[2:]))
arr = np.ndarray(shape=dims,
dtype=arr_dtype_number(arr, 1),
buffer=arr)
empties = [arr == '']
if not np.any(empties):
return arr
arr = arr.copy()
arr[empties] = ' '
return arr
| 12,083 | 28.048077 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/test_byteordercodes.py
|
''' Tests for byteorder module '''
from __future__ import division, print_function, absolute_import
import sys
from numpy.testing import assert_
from pytest import raises as assert_raises
import scipy.io.matlab.byteordercodes as sibc
def test_native():
native_is_le = sys.byteorder == 'little'
assert_(sibc.sys_is_le == native_is_le)
def test_to_numpy():
if sys.byteorder == 'little':
assert_(sibc.to_numpy_code('native') == '<')
assert_(sibc.to_numpy_code('swapped') == '>')
else:
assert_(sibc.to_numpy_code('native') == '>')
assert_(sibc.to_numpy_code('swapped') == '<')
assert_(sibc.to_numpy_code('native') == sibc.to_numpy_code('='))
assert_(sibc.to_numpy_code('big') == '>')
for code in ('little', '<', 'l', 'L', 'le'):
assert_(sibc.to_numpy_code(code) == '<')
for code in ('big', '>', 'b', 'B', 'be'):
assert_(sibc.to_numpy_code(code) == '>')
assert_raises(ValueError, sibc.to_numpy_code, 'silly string')
| 1,003 | 30.375 | 68 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/test_streams.py
|
""" Testing
"""
from __future__ import division, print_function, absolute_import
import os
import sys
import zlib
from io import BytesIO
if sys.version_info[0] >= 3:
cStringIO = BytesIO
else:
from cStringIO import StringIO as cStringIO
from tempfile import mkstemp
from contextlib import contextmanager
import numpy as np
from numpy.testing import assert_, assert_equal
from pytest import raises as assert_raises
from scipy.io.matlab.streams import (make_stream,
GenericStream, cStringStream, FileStream, ZlibInputStream,
_read_into, _read_string)
IS_PYPY = ('__pypy__' in sys.modules)
@contextmanager
def setup_test_file():
val = b'a\x00string'
fd, fname = mkstemp()
with os.fdopen(fd, 'wb') as fs:
fs.write(val)
with open(fname, 'rb') as fs:
gs = BytesIO(val)
cs = cStringIO(val)
yield fs, gs, cs
os.unlink(fname)
def test_make_stream():
with setup_test_file() as (fs, gs, cs):
# test stream initialization
assert_(isinstance(make_stream(gs), GenericStream))
if sys.version_info[0] < 3 and not IS_PYPY:
assert_(isinstance(make_stream(cs), cStringStream))
assert_(isinstance(make_stream(fs), FileStream))
def test_tell_seek():
with setup_test_file() as (fs, gs, cs):
for s in (fs, gs, cs):
st = make_stream(s)
res = st.seek(0)
assert_equal(res, 0)
assert_equal(st.tell(), 0)
res = st.seek(5)
assert_equal(res, 0)
assert_equal(st.tell(), 5)
res = st.seek(2, 1)
assert_equal(res, 0)
assert_equal(st.tell(), 7)
res = st.seek(-2, 2)
assert_equal(res, 0)
assert_equal(st.tell(), 6)
def test_read():
with setup_test_file() as (fs, gs, cs):
for s in (fs, gs, cs):
st = make_stream(s)
st.seek(0)
res = st.read(-1)
assert_equal(res, b'a\x00string')
st.seek(0)
res = st.read(4)
assert_equal(res, b'a\x00st')
# read into
st.seek(0)
res = _read_into(st, 4)
assert_equal(res, b'a\x00st')
res = _read_into(st, 4)
assert_equal(res, b'ring')
assert_raises(IOError, _read_into, st, 2)
# read alloc
st.seek(0)
res = _read_string(st, 4)
assert_equal(res, b'a\x00st')
res = _read_string(st, 4)
assert_equal(res, b'ring')
assert_raises(IOError, _read_string, st, 2)
class TestZlibInputStream(object):
def _get_data(self, size):
data = np.random.randint(0, 256, size).astype(np.uint8).tostring()
compressed_data = zlib.compress(data)
stream = BytesIO(compressed_data)
return stream, len(compressed_data), data
def test_read(self):
block_size = 131072
SIZES = [0, 1, 10, block_size//2, block_size-1,
block_size, block_size+1, 2*block_size-1]
READ_SIZES = [block_size//2, block_size-1,
block_size, block_size+1]
def check(size, read_size):
compressed_stream, compressed_data_len, data = self._get_data(size)
stream = ZlibInputStream(compressed_stream, compressed_data_len)
data2 = b''
so_far = 0
while True:
block = stream.read(min(read_size,
size - so_far))
if not block:
break
so_far += len(block)
data2 += block
assert_equal(data, data2)
for size in SIZES:
for read_size in READ_SIZES:
check(size, read_size)
def test_read_max_length(self):
size = 1234
data = np.random.randint(0, 256, size).astype(np.uint8).tostring()
compressed_data = zlib.compress(data)
compressed_stream = BytesIO(compressed_data + b"abbacaca")
stream = ZlibInputStream(compressed_stream, len(compressed_data))
stream.read(len(data))
assert_equal(compressed_stream.tell(), len(compressed_data))
assert_raises(IOError, stream.read, 1)
def test_seek(self):
compressed_stream, compressed_data_len, data = self._get_data(1024)
stream = ZlibInputStream(compressed_stream, compressed_data_len)
stream.seek(123)
p = 123
assert_equal(stream.tell(), p)
d1 = stream.read(11)
assert_equal(d1, data[p:p+11])
stream.seek(321, 1)
p = 123+11+321
assert_equal(stream.tell(), p)
d2 = stream.read(21)
assert_equal(d2, data[p:p+21])
stream.seek(641, 0)
p = 641
assert_equal(stream.tell(), p)
d3 = stream.read(11)
assert_equal(d3, data[p:p+11])
assert_raises(IOError, stream.seek, 10, 2)
assert_raises(IOError, stream.seek, -1, 1)
assert_raises(ValueError, stream.seek, 1, 123)
stream.seek(10000, 1)
assert_raises(IOError, stream.read, 12)
def test_all_data_read(self):
compressed_stream, compressed_data_len, data = self._get_data(1024)
stream = ZlibInputStream(compressed_stream, compressed_data_len)
assert_(not stream.all_data_read())
stream.seek(512)
assert_(not stream.all_data_read())
stream.seek(1024)
assert_(stream.all_data_read())
| 5,515 | 28.816216 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/afunc.m
|
function [a, b] = afunc(c, d)
% A function
a = c + 1;
b = d + 10;
| 66 | 12.4 | 29 |
m
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/test_miobase.py
|
""" Testing miobase module
"""
import numpy as np
from numpy.testing import assert_equal
from pytest import raises as assert_raises
from scipy.io.matlab.miobase import matdims
def test_matdims():
# Test matdims dimension finder
assert_equal(matdims(np.array(1)), (1, 1)) # numpy scalar
assert_equal(matdims(np.array([1])), (1, 1)) # 1d array, 1 element
assert_equal(matdims(np.array([1,2])), (2, 1)) # 1d array, 2 elements
assert_equal(matdims(np.array([[2],[3]])), (2, 1)) # 2d array, column vector
assert_equal(matdims(np.array([[2,3]])), (1, 2)) # 2d array, row vector
# 3d array, rowish vector
assert_equal(matdims(np.array([[[2,3]]])), (1, 1, 2))
assert_equal(matdims(np.array([])), (0, 0)) # empty 1d array
assert_equal(matdims(np.array([[]])), (0, 0)) # empty 2d
assert_equal(matdims(np.array([[[]]])), (0, 0, 0)) # empty 3d
# Optional argument flips 1-D shape behavior.
assert_equal(matdims(np.array([1,2]), 'row'), (1, 2)) # 1d array, 2 elements
# The argument has to make sense though
assert_raises(ValueError, matdims, np.array([1,2]), 'bizarre')
# Check empty sparse matrices get their own shape
from scipy.sparse import csr_matrix, csc_matrix
assert_equal(matdims(csr_matrix(np.zeros((3, 3)))), (3, 3))
assert_equal(matdims(csc_matrix(np.zeros((2, 2)))), (2, 2))
| 1,366 | 41.71875 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/save_matfile.m
|
function save_matfile(test_name, v)
% saves variable passed in m with filename from prefix
global FILEPREFIX FILESUFFIX
eval([test_name ' = v;']);
save([FILEPREFIX test_name FILESUFFIX], test_name)
| 200 | 32.5 | 54 |
m
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/gen_mat5files.m
|
% Generates mat files for loadmat unit tests
% This is the version for matlab 5 and higher
% Uses save_matfile.m function
% work out matlab version and file suffix for test files
global FILEPREFIX FILESUFFIX
FILEPREFIX = [fullfile(pwd, 'data') filesep];
temp = ver('MATLAB');
mlv = temp.Version;
FILESUFFIX = ['_' mlv '_' computer '.mat'];
% basic double array
theta = 0:pi/4:2*pi;
save_matfile('testdouble', theta);
% string
save_matfile('teststring', '"Do nine men interpret?" "Nine men," I nod.')
% complex
save_matfile('testcomplex', cos(theta) + 1j*sin(theta));
% asymmetric array to check indexing
a = zeros(3, 5);
a(:,1) = [1:3]';
a(1,:) = 1:5;
% 2D matrix
save_matfile('testmatrix', a);
% minus number - tests signed int
save_matfile('testminus', -1);
% single character
save_matfile('testonechar', 'r');
% string array
save_matfile('teststringarray', ['one '; 'two '; 'three']);
% sparse array
save_matfile('testsparse', sparse(a));
% sparse complex array
b = sparse(a);
b(1,1) = b(1,1) + j;
save_matfile('testsparsecomplex', b);
% Two variables in same file
save([FILEPREFIX 'testmulti' FILESUFFIX], 'a', 'theta')
% struct
save_matfile('teststruct', ...
struct('stringfield','Rats live on no evil star.',...
'doublefield',[sqrt(2) exp(1) pi],...
'complexfield',(1+1j)*[sqrt(2) exp(1) pi]));
% cell
save_matfile('testcell', ...
{['This cell contains this string and 3 arrays of increasing' ...
' length'], 1., 1.:2., 1.:3.});
% scalar cell
save_matfile('testscalarcell', {1})
% Empty cells in two cell matrices
save_matfile('testemptycell', {1, 2, [], [], 3});
% 3D matrix
save_matfile('test3dmatrix', reshape(1:24,[2 3 4]))
% nested cell array
save_matfile('testcellnest', {1, {2, 3, {4, 5}}});
% nested struct
save_matfile('teststructnest', struct('one', 1, 'two', ...
struct('three', 'number 3')));
% array of struct
save_matfile('teststructarr', [struct('one', 1, 'two', 2) ...
struct('one', 'number 1', 'two', 'number 2')]);
% matlab object
save_matfile('testobject', inline('x'))
% array of matlab objects
%save_matfile('testobjarr', [inline('x') inline('x')])
% unicode test
if str2num(mlv) > 7 % function added 7.0.1
fid = fopen([FILEPREFIX 'japanese_utf8.txt']);
from_japan = fread(fid, 'uint8')';
fclose(fid);
save_matfile('testunicode', native2unicode(from_japan, 'utf-8'));
end
% func
if str2num(mlv) > 7 % function pointers added recently
func = @afunc;
save_matfile('testfunc', func);
end
| 2,485 | 23.86 | 73 |
m
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/test_mio_funcs.py
|
''' Jottings to work out format for __function_workspace__ matrix at end
of mat file.
'''
from __future__ import division, print_function, absolute_import
import os.path
import sys
import io
from numpy.compat import asstr
from scipy.io.matlab.mio5 import (MatlabObject, MatFile5Writer,
MatFile5Reader, MatlabFunction)
test_data_path = os.path.join(os.path.dirname(__file__), 'data')
def read_minimat_vars(rdr):
rdr.initialize_read()
mdict = {'__globals__': []}
i = 0
while not rdr.end_of_stream():
hdr, next_position = rdr.read_var_header()
name = asstr(hdr.name)
if name == '':
name = 'var_%d' % i
i += 1
res = rdr.read_var_array(hdr, process=False)
rdr.mat_stream.seek(next_position)
mdict[name] = res
if hdr.is_global:
mdict['__globals__'].append(name)
return mdict
def read_workspace_vars(fname):
fp = open(fname, 'rb')
rdr = MatFile5Reader(fp, struct_as_record=True)
vars = rdr.get_variables()
fws = vars['__function_workspace__']
ws_bs = io.BytesIO(fws.tostring())
ws_bs.seek(2)
rdr.mat_stream = ws_bs
# Guess byte order.
mi = rdr.mat_stream.read(2)
rdr.byte_order = mi == b'IM' and '<' or '>'
rdr.mat_stream.read(4) # presumably byte padding
mdict = read_minimat_vars(rdr)
fp.close()
return mdict
def test_jottings():
# example
fname = os.path.join(test_data_path, 'parabola.mat')
ws_vars = read_workspace_vars(fname)
| 1,551 | 25.758621 | 72 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/test_mio_utils.py
|
""" Testing
"""
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import assert_array_equal, assert_array_almost_equal, \
assert_
from scipy.io.matlab.mio_utils import squeeze_element, chars_to_strings
def test_squeeze_element():
a = np.zeros((1,3))
assert_array_equal(np.squeeze(a), squeeze_element(a))
# 0d output from squeeze gives scalar
sq_int = squeeze_element(np.zeros((1,1), dtype=float))
assert_(isinstance(sq_int, float))
# Unless it's a structured array
sq_sa = squeeze_element(np.zeros((1,1),dtype=[('f1', 'f')]))
assert_(isinstance(sq_sa, np.ndarray))
def test_chars_strings():
# chars as strings
strings = ['learn ', 'python', 'fast ', 'here ']
str_arr = np.array(strings, dtype='U6') # shape (4,)
chars = [list(s) for s in strings]
char_arr = np.array(chars, dtype='U1') # shape (4,6)
assert_array_equal(chars_to_strings(char_arr), str_arr)
ca2d = char_arr.reshape((2,2,6))
sa2d = str_arr.reshape((2,2))
assert_array_equal(chars_to_strings(ca2d), sa2d)
ca3d = char_arr.reshape((1,2,2,6))
sa3d = str_arr.reshape((1,2,2))
assert_array_equal(chars_to_strings(ca3d), sa3d)
# Fortran ordered arrays
char_arrf = np.array(chars, dtype='U1', order='F') # shape (4,6)
assert_array_equal(chars_to_strings(char_arrf), str_arr)
# empty array
arr = np.array([['']], dtype='U1')
out_arr = np.array([''], dtype='U1')
assert_array_equal(chars_to_strings(arr), out_arr)
| 1,549 | 31.978723 | 74 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/test_mio5_utils.py
|
""" Testing mio5_utils Cython module
"""
from __future__ import division, print_function, absolute_import
import sys
from io import BytesIO
cStringIO = BytesIO
import numpy as np
from numpy.testing import assert_array_equal, assert_equal, assert_
from pytest import raises as assert_raises
from scipy._lib.six import u
import scipy.io.matlab.byteordercodes as boc
import scipy.io.matlab.streams as streams
import scipy.io.matlab.mio5_params as mio5p
import scipy.io.matlab.mio5_utils as m5u
def test_byteswap():
for val in (
1,
0x100,
0x10000):
a = np.array(val, dtype=np.uint32)
b = a.byteswap()
c = m5u.byteswap_u4(a)
assert_equal(b.item(), c)
d = m5u.byteswap_u4(c)
assert_equal(a.item(), d)
def _make_tag(base_dt, val, mdtype, sde=False):
''' Makes a simple matlab tag, full or sde '''
base_dt = np.dtype(base_dt)
bo = boc.to_numpy_code(base_dt.byteorder)
byte_count = base_dt.itemsize
if not sde:
udt = bo + 'u4'
padding = 8 - (byte_count % 8)
all_dt = [('mdtype', udt),
('byte_count', udt),
('val', base_dt)]
if padding:
all_dt.append(('padding', 'u1', padding))
else: # is sde
udt = bo + 'u2'
padding = 4-byte_count
if bo == '<': # little endian
all_dt = [('mdtype', udt),
('byte_count', udt),
('val', base_dt)]
else: # big endian
all_dt = [('byte_count', udt),
('mdtype', udt),
('val', base_dt)]
if padding:
all_dt.append(('padding', 'u1', padding))
tag = np.zeros((1,), dtype=all_dt)
tag['mdtype'] = mdtype
tag['byte_count'] = byte_count
tag['val'] = val
return tag
def _write_stream(stream, *strings):
stream.truncate(0)
stream.seek(0)
for s in strings:
stream.write(s)
stream.seek(0)
def _make_readerlike(stream, byte_order=boc.native_code):
class R(object):
pass
r = R()
r.mat_stream = stream
r.byte_order = byte_order
r.struct_as_record = True
r.uint16_codec = sys.getdefaultencoding()
r.chars_as_strings = False
r.mat_dtype = False
r.squeeze_me = False
return r
def test_read_tag():
# mainly to test errors
# make reader-like thing
str_io = BytesIO()
r = _make_readerlike(str_io)
c_reader = m5u.VarReader5(r)
# This works for StringIO but _not_ cStringIO
assert_raises(IOError, c_reader.read_tag)
# bad SDE
tag = _make_tag('i4', 1, mio5p.miINT32, sde=True)
tag['byte_count'] = 5
_write_stream(str_io, tag.tostring())
assert_raises(ValueError, c_reader.read_tag)
def test_read_stream():
tag = _make_tag('i4', 1, mio5p.miINT32, sde=True)
tag_str = tag.tostring()
str_io = cStringIO(tag_str)
st = streams.make_stream(str_io)
s = streams._read_into(st, tag.itemsize)
assert_equal(s, tag.tostring())
def test_read_numeric():
# make reader-like thing
str_io = cStringIO()
r = _make_readerlike(str_io)
# check simplest of tags
for base_dt, val, mdtype in (('u2', 30, mio5p.miUINT16),
('i4', 1, mio5p.miINT32),
('i2', -1, mio5p.miINT16)):
for byte_code in ('<', '>'):
r.byte_order = byte_code
c_reader = m5u.VarReader5(r)
assert_equal(c_reader.little_endian, byte_code == '<')
assert_equal(c_reader.is_swapped, byte_code != boc.native_code)
for sde_f in (False, True):
dt = np.dtype(base_dt).newbyteorder(byte_code)
a = _make_tag(dt, val, mdtype, sde_f)
a_str = a.tostring()
_write_stream(str_io, a_str)
el = c_reader.read_numeric()
assert_equal(el, val)
# two sequential reads
_write_stream(str_io, a_str, a_str)
el = c_reader.read_numeric()
assert_equal(el, val)
el = c_reader.read_numeric()
assert_equal(el, val)
def test_read_numeric_writeable():
# make reader-like thing
str_io = cStringIO()
r = _make_readerlike(str_io, '<')
c_reader = m5u.VarReader5(r)
dt = np.dtype('<u2')
a = _make_tag(dt, 30, mio5p.miUINT16, 0)
a_str = a.tostring()
_write_stream(str_io, a_str)
el = c_reader.read_numeric()
assert_(el.flags.writeable is True)
def test_zero_byte_string():
# Tests hack to allow chars of non-zero length, but 0 bytes
# make reader-like thing
str_io = cStringIO()
r = _make_readerlike(str_io, boc.native_code)
c_reader = m5u.VarReader5(r)
tag_dt = np.dtype([('mdtype', 'u4'), ('byte_count', 'u4')])
tag = np.zeros((1,), dtype=tag_dt)
tag['mdtype'] = mio5p.miINT8
tag['byte_count'] = 1
hdr = m5u.VarHeader5()
# Try when string is 1 length
hdr.set_dims([1,])
_write_stream(str_io, tag.tostring() + b' ')
str_io.seek(0)
val = c_reader.read_char(hdr)
assert_equal(val, u(' '))
# Now when string has 0 bytes 1 length
tag['byte_count'] = 0
_write_stream(str_io, tag.tostring())
str_io.seek(0)
val = c_reader.read_char(hdr)
assert_equal(val, u(' '))
# Now when string has 0 bytes 4 length
str_io.seek(0)
hdr.set_dims([4,])
val = c_reader.read_char(hdr)
assert_array_equal(val, [u(' ')] * 4)
| 5,536 | 28.768817 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/test_mio.py
|
# -*- coding: latin-1 -*-
''' Nose test generators
Need function load / save / roundtrip tests
'''
from __future__ import division, print_function, absolute_import
import os
from collections import OrderedDict
from os.path import join as pjoin, dirname
from glob import glob
from io import BytesIO
from tempfile import mkdtemp
from scipy._lib.six import u, text_type, string_types
import warnings
import shutil
import gzip
from numpy.testing import (assert_array_equal, assert_array_almost_equal,
assert_equal, assert_)
from pytest import raises as assert_raises
from scipy._lib._numpy_compat import suppress_warnings
import numpy as np
from numpy import array
import scipy.sparse as SP
import scipy.io.matlab.byteordercodes as boc
from scipy.io.matlab.miobase import matdims, MatWriteError, MatReadError
from scipy.io.matlab.mio import (mat_reader_factory, loadmat, savemat, whosmat)
from scipy.io.matlab.mio5 import (MatlabObject, MatFile5Writer, MatFile5Reader,
MatlabFunction, varmats_from_mat,
to_writeable, EmptyStructMarker)
from scipy.io.matlab import mio5_params as mio5p
test_data_path = pjoin(dirname(__file__), 'data')
def mlarr(*args, **kwargs):
"""Convenience function to return matlab-compatible 2D array."""
arr = np.array(*args, **kwargs)
arr.shape = matdims(arr)
return arr
# Define cases to test
theta = np.pi/4*np.arange(9,dtype=float).reshape(1,9)
case_table4 = [
{'name': 'double',
'classes': {'testdouble': 'double'},
'expected': {'testdouble': theta}
}]
case_table4.append(
{'name': 'string',
'classes': {'teststring': 'char'},
'expected': {'teststring':
array([u('"Do nine men interpret?" "Nine men," I nod.')])}
})
case_table4.append(
{'name': 'complex',
'classes': {'testcomplex': 'double'},
'expected': {'testcomplex': np.cos(theta) + 1j*np.sin(theta)}
})
A = np.zeros((3,5))
A[0] = list(range(1,6))
A[:,0] = list(range(1,4))
case_table4.append(
{'name': 'matrix',
'classes': {'testmatrix': 'double'},
'expected': {'testmatrix': A},
})
case_table4.append(
{'name': 'sparse',
'classes': {'testsparse': 'sparse'},
'expected': {'testsparse': SP.coo_matrix(A)},
})
B = A.astype(complex)
B[0,0] += 1j
case_table4.append(
{'name': 'sparsecomplex',
'classes': {'testsparsecomplex': 'sparse'},
'expected': {'testsparsecomplex': SP.coo_matrix(B)},
})
case_table4.append(
{'name': 'multi',
'classes': {'theta': 'double', 'a': 'double'},
'expected': {'theta': theta, 'a': A},
})
case_table4.append(
{'name': 'minus',
'classes': {'testminus': 'double'},
'expected': {'testminus': mlarr(-1)},
})
case_table4.append(
{'name': 'onechar',
'classes': {'testonechar': 'char'},
'expected': {'testonechar': array([u('r')])},
})
# Cell arrays stored as object arrays
CA = mlarr(( # tuple for object array creation
[],
mlarr([1]),
mlarr([[1,2]]),
mlarr([[1,2,3]])), dtype=object).reshape(1,-1)
CA[0,0] = array(
[u('This cell contains this string and 3 arrays of increasing length')])
case_table5 = [
{'name': 'cell',
'classes': {'testcell': 'cell'},
'expected': {'testcell': CA}}]
CAE = mlarr(( # tuple for object array creation
mlarr(1),
mlarr(2),
mlarr([]),
mlarr([]),
mlarr(3)), dtype=object).reshape(1,-1)
objarr = np.empty((1,1),dtype=object)
objarr[0,0] = mlarr(1)
case_table5.append(
{'name': 'scalarcell',
'classes': {'testscalarcell': 'cell'},
'expected': {'testscalarcell': objarr}
})
case_table5.append(
{'name': 'emptycell',
'classes': {'testemptycell': 'cell'},
'expected': {'testemptycell': CAE}})
case_table5.append(
{'name': 'stringarray',
'classes': {'teststringarray': 'char'},
'expected': {'teststringarray': array(
[u('one '), u('two '), u('three')])},
})
case_table5.append(
{'name': '3dmatrix',
'classes': {'test3dmatrix': 'double'},
'expected': {
'test3dmatrix': np.transpose(np.reshape(list(range(1,25)), (4,3,2)))}
})
st_sub_arr = array([np.sqrt(2),np.exp(1),np.pi]).reshape(1,3)
dtype = [(n, object) for n in ['stringfield', 'doublefield', 'complexfield']]
st1 = np.zeros((1,1), dtype)
st1['stringfield'][0,0] = array([u('Rats live on no evil star.')])
st1['doublefield'][0,0] = st_sub_arr
st1['complexfield'][0,0] = st_sub_arr * (1 + 1j)
case_table5.append(
{'name': 'struct',
'classes': {'teststruct': 'struct'},
'expected': {'teststruct': st1}
})
CN = np.zeros((1,2), dtype=object)
CN[0,0] = mlarr(1)
CN[0,1] = np.zeros((1,3), dtype=object)
CN[0,1][0,0] = mlarr(2, dtype=np.uint8)
CN[0,1][0,1] = mlarr([[3]], dtype=np.uint8)
CN[0,1][0,2] = np.zeros((1,2), dtype=object)
CN[0,1][0,2][0,0] = mlarr(4, dtype=np.uint8)
CN[0,1][0,2][0,1] = mlarr(5, dtype=np.uint8)
case_table5.append(
{'name': 'cellnest',
'classes': {'testcellnest': 'cell'},
'expected': {'testcellnest': CN},
})
st2 = np.empty((1,1), dtype=[(n, object) for n in ['one', 'two']])
st2[0,0]['one'] = mlarr(1)
st2[0,0]['two'] = np.empty((1,1), dtype=[('three', object)])
st2[0,0]['two'][0,0]['three'] = array([u('number 3')])
case_table5.append(
{'name': 'structnest',
'classes': {'teststructnest': 'struct'},
'expected': {'teststructnest': st2}
})
a = np.empty((1,2), dtype=[(n, object) for n in ['one', 'two']])
a[0,0]['one'] = mlarr(1)
a[0,0]['two'] = mlarr(2)
a[0,1]['one'] = array([u('number 1')])
a[0,1]['two'] = array([u('number 2')])
case_table5.append(
{'name': 'structarr',
'classes': {'teststructarr': 'struct'},
'expected': {'teststructarr': a}
})
ODT = np.dtype([(n, object) for n in
['expr', 'inputExpr', 'args',
'isEmpty', 'numArgs', 'version']])
MO = MatlabObject(np.zeros((1,1), dtype=ODT), 'inline')
m0 = MO[0,0]
m0['expr'] = array([u('x')])
m0['inputExpr'] = array([u(' x = INLINE_INPUTS_{1};')])
m0['args'] = array([u('x')])
m0['isEmpty'] = mlarr(0)
m0['numArgs'] = mlarr(1)
m0['version'] = mlarr(1)
case_table5.append(
{'name': 'object',
'classes': {'testobject': 'object'},
'expected': {'testobject': MO}
})
fp_u_str = open(pjoin(test_data_path, 'japanese_utf8.txt'), 'rb')
u_str = fp_u_str.read().decode('utf-8')
fp_u_str.close()
case_table5.append(
{'name': 'unicode',
'classes': {'testunicode': 'char'},
'expected': {'testunicode': array([u_str])}
})
case_table5.append(
{'name': 'sparse',
'classes': {'testsparse': 'sparse'},
'expected': {'testsparse': SP.coo_matrix(A)},
})
case_table5.append(
{'name': 'sparsecomplex',
'classes': {'testsparsecomplex': 'sparse'},
'expected': {'testsparsecomplex': SP.coo_matrix(B)},
})
case_table5.append(
{'name': 'bool',
'classes': {'testbools': 'logical'},
'expected': {'testbools':
array([[True], [False]])},
})
case_table5_rt = case_table5[:]
# Inline functions can't be concatenated in matlab, so RT only
case_table5_rt.append(
{'name': 'objectarray',
'classes': {'testobjectarray': 'object'},
'expected': {'testobjectarray': np.repeat(MO, 2).reshape(1,2)}})
def types_compatible(var1, var2):
"""Check if types are same or compatible.
0-D numpy scalars are compatible with bare python scalars.
"""
type1 = type(var1)
type2 = type(var2)
if type1 is type2:
return True
if type1 is np.ndarray and var1.shape == ():
return type(var1.item()) is type2
if type2 is np.ndarray and var2.shape == ():
return type(var2.item()) is type1
return False
def _check_level(label, expected, actual):
""" Check one level of a potentially nested array """
if SP.issparse(expected): # allow different types of sparse matrices
assert_(SP.issparse(actual))
assert_array_almost_equal(actual.todense(),
expected.todense(),
err_msg=label,
decimal=5)
return
# Check types are as expected
assert_(types_compatible(expected, actual),
"Expected type %s, got %s at %s" %
(type(expected), type(actual), label))
# A field in a record array may not be an ndarray
# A scalar from a record array will be type np.void
if not isinstance(expected,
(np.void, np.ndarray, MatlabObject)):
assert_equal(expected, actual)
return
# This is an ndarray-like thing
assert_(expected.shape == actual.shape,
msg='Expected shape %s, got %s at %s' % (expected.shape,
actual.shape,
label))
ex_dtype = expected.dtype
if ex_dtype.hasobject: # array of objects
if isinstance(expected, MatlabObject):
assert_equal(expected.classname, actual.classname)
for i, ev in enumerate(expected):
level_label = "%s, [%d], " % (label, i)
_check_level(level_label, ev, actual[i])
return
if ex_dtype.fields: # probably recarray
for fn in ex_dtype.fields:
level_label = "%s, field %s, " % (label, fn)
_check_level(level_label,
expected[fn], actual[fn])
return
if ex_dtype.type in (text_type, # string or bool
np.unicode_,
np.bool_):
assert_equal(actual, expected, err_msg=label)
return
# Something numeric
assert_array_almost_equal(actual, expected, err_msg=label, decimal=5)
def _load_check_case(name, files, case):
for file_name in files:
matdict = loadmat(file_name, struct_as_record=True)
label = "test %s; file %s" % (name, file_name)
for k, expected in case.items():
k_label = "%s, variable %s" % (label, k)
assert_(k in matdict, "Missing key at %s" % k_label)
_check_level(k_label, expected, matdict[k])
def _whos_check_case(name, files, case, classes):
for file_name in files:
label = "test %s; file %s" % (name, file_name)
whos = whosmat(file_name)
expected_whos = []
for k, expected in case.items():
expected_whos.append((k, expected.shape, classes[k]))
whos.sort()
expected_whos.sort()
assert_equal(whos, expected_whos,
"%s: %r != %r" % (label, whos, expected_whos)
)
# Round trip tests
def _rt_check_case(name, expected, format):
mat_stream = BytesIO()
savemat(mat_stream, expected, format=format)
mat_stream.seek(0)
_load_check_case(name, [mat_stream], expected)
# generator for load tests
def test_load():
for case in case_table4 + case_table5:
name = case['name']
expected = case['expected']
filt = pjoin(test_data_path, 'test%s_*.mat' % name)
files = glob(filt)
assert_(len(files) > 0,
"No files for test %s using filter %s" % (name, filt))
_load_check_case(name, files, expected)
# generator for whos tests
def test_whos():
for case in case_table4 + case_table5:
name = case['name']
expected = case['expected']
classes = case['classes']
filt = pjoin(test_data_path, 'test%s_*.mat' % name)
files = glob(filt)
assert_(len(files) > 0,
"No files for test %s using filter %s" % (name, filt))
_whos_check_case(name, files, expected, classes)
# generator for round trip tests
def test_round_trip():
for case in case_table4 + case_table5_rt:
case_table4_names = [case['name'] for case in case_table4]
name = case['name'] + '_round_trip'
expected = case['expected']
for format in (['4', '5'] if case['name'] in case_table4_names else ['5']):
_rt_check_case(name, expected, format)
def test_gzip_simple():
xdense = np.zeros((20,20))
xdense[2,3] = 2.3
xdense[4,5] = 4.5
x = SP.csc_matrix(xdense)
name = 'gzip_test'
expected = {'x':x}
format = '4'
tmpdir = mkdtemp()
try:
fname = pjoin(tmpdir,name)
mat_stream = gzip.open(fname,mode='wb')
savemat(mat_stream, expected, format=format)
mat_stream.close()
mat_stream = gzip.open(fname,mode='rb')
actual = loadmat(mat_stream, struct_as_record=True)
mat_stream.close()
finally:
shutil.rmtree(tmpdir)
assert_array_almost_equal(actual['x'].todense(),
expected['x'].todense(),
err_msg=repr(actual))
def test_multiple_open():
# Ticket #1039, on Windows: check that files are not left open
tmpdir = mkdtemp()
try:
x = dict(x=np.zeros((2, 2)))
fname = pjoin(tmpdir, "a.mat")
# Check that file is not left open
savemat(fname, x)
os.unlink(fname)
savemat(fname, x)
loadmat(fname)
os.unlink(fname)
# Check that stream is left open
f = open(fname, 'wb')
savemat(f, x)
f.seek(0)
f.close()
f = open(fname, 'rb')
loadmat(f)
f.seek(0)
f.close()
finally:
shutil.rmtree(tmpdir)
def test_mat73():
# Check any hdf5 files raise an error
filenames = glob(
pjoin(test_data_path, 'testhdf5*.mat'))
assert_(len(filenames) > 0)
for filename in filenames:
fp = open(filename, 'rb')
assert_raises(NotImplementedError,
loadmat,
fp,
struct_as_record=True)
fp.close()
def test_warnings():
# This test is an echo of the previous behavior, which was to raise a
# warning if the user triggered a search for mat files on the Python system
# path. We can remove the test in the next version after upcoming (0.13)
fname = pjoin(test_data_path, 'testdouble_7.1_GLNX86.mat')
with warnings.catch_warnings():
warnings.simplefilter('error')
# This should not generate a warning
mres = loadmat(fname, struct_as_record=True)
# This neither
mres = loadmat(fname, struct_as_record=False)
def test_regression_653():
# Saving a dictionary with only invalid keys used to raise an error. Now we
# save this as an empty struct in matlab space.
sio = BytesIO()
savemat(sio, {'d':{1:2}}, format='5')
back = loadmat(sio)['d']
# Check we got an empty struct equivalent
assert_equal(back.shape, (1,1))
assert_equal(back.dtype, np.dtype(object))
assert_(back[0,0] is None)
def test_structname_len():
# Test limit for length of field names in structs
lim = 31
fldname = 'a' * lim
st1 = np.zeros((1,1), dtype=[(fldname, object)])
savemat(BytesIO(), {'longstruct': st1}, format='5')
fldname = 'a' * (lim+1)
st1 = np.zeros((1,1), dtype=[(fldname, object)])
assert_raises(ValueError, savemat, BytesIO(),
{'longstruct': st1}, format='5')
def test_4_and_long_field_names_incompatible():
# Long field names option not supported in 4
my_struct = np.zeros((1,1),dtype=[('my_fieldname',object)])
assert_raises(ValueError, savemat, BytesIO(),
{'my_struct':my_struct}, format='4', long_field_names=True)
def test_long_field_names():
# Test limit for length of field names in structs
lim = 63
fldname = 'a' * lim
st1 = np.zeros((1,1), dtype=[(fldname, object)])
savemat(BytesIO(), {'longstruct': st1}, format='5',long_field_names=True)
fldname = 'a' * (lim+1)
st1 = np.zeros((1,1), dtype=[(fldname, object)])
assert_raises(ValueError, savemat, BytesIO(),
{'longstruct': st1}, format='5',long_field_names=True)
def test_long_field_names_in_struct():
# Regression test - long_field_names was erased if you passed a struct
# within a struct
lim = 63
fldname = 'a' * lim
cell = np.ndarray((1,2),dtype=object)
st1 = np.zeros((1,1), dtype=[(fldname, object)])
cell[0,0] = st1
cell[0,1] = st1
savemat(BytesIO(), {'longstruct': cell}, format='5',long_field_names=True)
#
# Check to make sure it fails with long field names off
#
assert_raises(ValueError, savemat, BytesIO(),
{'longstruct': cell}, format='5', long_field_names=False)
def test_cell_with_one_thing_in_it():
# Regression test - make a cell array that's 1 x 2 and put two
# strings in it. It works. Make a cell array that's 1 x 1 and put
# a string in it. It should work but, in the old days, it didn't.
cells = np.ndarray((1,2),dtype=object)
cells[0,0] = 'Hello'
cells[0,1] = 'World'
savemat(BytesIO(), {'x': cells}, format='5')
cells = np.ndarray((1,1),dtype=object)
cells[0,0] = 'Hello, world'
savemat(BytesIO(), {'x': cells}, format='5')
def test_writer_properties():
# Tests getting, setting of properties of matrix writer
mfw = MatFile5Writer(BytesIO())
assert_equal(mfw.global_vars, [])
mfw.global_vars = ['avar']
assert_equal(mfw.global_vars, ['avar'])
assert_equal(mfw.unicode_strings, False)
mfw.unicode_strings = True
assert_equal(mfw.unicode_strings, True)
assert_equal(mfw.long_field_names, False)
mfw.long_field_names = True
assert_equal(mfw.long_field_names, True)
def test_use_small_element():
# Test whether we're using small data element or not
sio = BytesIO()
wtr = MatFile5Writer(sio)
# First check size for no sde for name
arr = np.zeros(10)
wtr.put_variables({'aaaaa': arr})
w_sz = len(sio.getvalue())
# Check small name results in largish difference in size
sio.truncate(0)
sio.seek(0)
wtr.put_variables({'aaaa': arr})
assert_(w_sz - len(sio.getvalue()) > 4)
# Whereas increasing name size makes less difference
sio.truncate(0)
sio.seek(0)
wtr.put_variables({'aaaaaa': arr})
assert_(len(sio.getvalue()) - w_sz < 4)
def test_save_dict():
# Test that dict can be saved (as recarray), loaded as matstruct
dict_types = ((dict, False), (OrderedDict, True),)
ab_exp = np.array([[(1, 2)]], dtype=[('a', object), ('b', object)])
ba_exp = np.array([[(2, 1)]], dtype=[('b', object), ('a', object)])
for dict_type, is_ordered in dict_types:
# Initialize with tuples to keep order for OrderedDict
d = dict_type([('a', 1), ('b', 2)])
stream = BytesIO()
savemat(stream, {'dict': d})
stream.seek(0)
vals = loadmat(stream)['dict']
assert_equal(set(vals.dtype.names), set(['a', 'b']))
if is_ordered: # Input was ordered, output in ab order
assert_array_equal(vals, ab_exp)
else: # Not ordered input, either order output
if vals.dtype.names[0] == 'a':
assert_array_equal(vals, ab_exp)
else:
assert_array_equal(vals, ba_exp)
def test_1d_shape():
# New 5 behavior is 1D -> row vector
arr = np.arange(5)
for format in ('4', '5'):
# Column is the default
stream = BytesIO()
savemat(stream, {'oned': arr}, format=format)
vals = loadmat(stream)
assert_equal(vals['oned'].shape, (1, 5))
# can be explicitly 'column' for oned_as
stream = BytesIO()
savemat(stream, {'oned':arr},
format=format,
oned_as='column')
vals = loadmat(stream)
assert_equal(vals['oned'].shape, (5,1))
# but different from 'row'
stream = BytesIO()
savemat(stream, {'oned':arr},
format=format,
oned_as='row')
vals = loadmat(stream)
assert_equal(vals['oned'].shape, (1,5))
def test_compression():
arr = np.zeros(100).reshape((5,20))
arr[2,10] = 1
stream = BytesIO()
savemat(stream, {'arr':arr})
raw_len = len(stream.getvalue())
vals = loadmat(stream)
assert_array_equal(vals['arr'], arr)
stream = BytesIO()
savemat(stream, {'arr':arr}, do_compression=True)
compressed_len = len(stream.getvalue())
vals = loadmat(stream)
assert_array_equal(vals['arr'], arr)
assert_(raw_len > compressed_len)
# Concatenate, test later
arr2 = arr.copy()
arr2[0,0] = 1
stream = BytesIO()
savemat(stream, {'arr':arr, 'arr2':arr2}, do_compression=False)
vals = loadmat(stream)
assert_array_equal(vals['arr2'], arr2)
stream = BytesIO()
savemat(stream, {'arr':arr, 'arr2':arr2}, do_compression=True)
vals = loadmat(stream)
assert_array_equal(vals['arr2'], arr2)
def test_single_object():
stream = BytesIO()
savemat(stream, {'A':np.array(1, dtype=object)})
def test_skip_variable():
# Test skipping over the first of two variables in a MAT file
# using mat_reader_factory and put_variables to read them in.
#
# This is a regression test of a problem that's caused by
# using the compressed file reader seek instead of the raw file
# I/O seek when skipping over a compressed chunk.
#
# The problem arises when the chunk is large: this file has
# a 256x256 array of random (uncompressible) doubles.
#
filename = pjoin(test_data_path,'test_skip_variable.mat')
#
# Prove that it loads with loadmat
#
d = loadmat(filename, struct_as_record=True)
assert_('first' in d)
assert_('second' in d)
#
# Make the factory
#
factory, file_opened = mat_reader_factory(filename, struct_as_record=True)
#
# This is where the factory breaks with an error in MatMatrixGetter.to_next
#
d = factory.get_variables('second')
assert_('second' in d)
factory.mat_stream.close()
def test_empty_struct():
# ticket 885
filename = pjoin(test_data_path,'test_empty_struct.mat')
# before ticket fix, this would crash with ValueError, empty data
# type
d = loadmat(filename, struct_as_record=True)
a = d['a']
assert_equal(a.shape, (1,1))
assert_equal(a.dtype, np.dtype(object))
assert_(a[0,0] is None)
stream = BytesIO()
arr = np.array((), dtype='U')
# before ticket fix, this used to give data type not understood
savemat(stream, {'arr':arr})
d = loadmat(stream)
a2 = d['arr']
assert_array_equal(a2, arr)
def test_save_empty_dict():
# saving empty dict also gives empty struct
stream = BytesIO()
savemat(stream, {'arr': {}})
d = loadmat(stream)
a = d['arr']
assert_equal(a.shape, (1,1))
assert_equal(a.dtype, np.dtype(object))
assert_(a[0,0] is None)
def assert_any_equal(output, alternatives):
""" Assert `output` is equal to at least one element in `alternatives`
"""
one_equal = False
for expected in alternatives:
if np.all(output == expected):
one_equal = True
break
assert_(one_equal)
def test_to_writeable():
# Test to_writeable function
res = to_writeable(np.array([1])) # pass through ndarrays
assert_equal(res.shape, (1,))
assert_array_equal(res, 1)
# Dict fields can be written in any order
expected1 = np.array([(1, 2)], dtype=[('a', '|O8'), ('b', '|O8')])
expected2 = np.array([(2, 1)], dtype=[('b', '|O8'), ('a', '|O8')])
alternatives = (expected1, expected2)
assert_any_equal(to_writeable({'a':1,'b':2}), alternatives)
# Fields with underscores discarded
assert_any_equal(to_writeable({'a':1,'b':2, '_c':3}), alternatives)
# Not-string fields discarded
assert_any_equal(to_writeable({'a':1,'b':2, 100:3}), alternatives)
# String fields that are valid Python identifiers discarded
assert_any_equal(to_writeable({'a':1,'b':2, '99':3}), alternatives)
# Object with field names is equivalent
class klass(object):
pass
c = klass
c.a = 1
c.b = 2
assert_any_equal(to_writeable(c), alternatives)
# empty list and tuple go to empty array
res = to_writeable([])
assert_equal(res.shape, (0,))
assert_equal(res.dtype.type, np.float64)
res = to_writeable(())
assert_equal(res.shape, (0,))
assert_equal(res.dtype.type, np.float64)
# None -> None
assert_(to_writeable(None) is None)
# String to strings
assert_equal(to_writeable('a string').dtype.type, np.str_)
# Scalars to numpy to numpy scalars
res = to_writeable(1)
assert_equal(res.shape, ())
assert_equal(res.dtype.type, np.array(1).dtype.type)
assert_array_equal(res, 1)
# Empty dict returns EmptyStructMarker
assert_(to_writeable({}) is EmptyStructMarker)
# Object does not have (even empty) __dict__
assert_(to_writeable(object()) is None)
# Custom object does have empty __dict__, returns EmptyStructMarker
class C(object):
pass
assert_(to_writeable(c()) is EmptyStructMarker)
# dict keys with legal characters are convertible
res = to_writeable({'a': 1})['a']
assert_equal(res.shape, (1,))
assert_equal(res.dtype.type, np.object_)
# Only fields with illegal characters, falls back to EmptyStruct
assert_(to_writeable({'1':1}) is EmptyStructMarker)
assert_(to_writeable({'_a':1}) is EmptyStructMarker)
# Unless there are valid fields, in which case structured array
assert_equal(to_writeable({'1':1, 'f': 2}),
np.array([(2,)], dtype=[('f', '|O8')]))
def test_recarray():
# check roundtrip of structured array
dt = [('f1', 'f8'),
('f2', 'S10')]
arr = np.zeros((2,), dtype=dt)
arr[0]['f1'] = 0.5
arr[0]['f2'] = 'python'
arr[1]['f1'] = 99
arr[1]['f2'] = 'not perl'
stream = BytesIO()
savemat(stream, {'arr': arr})
d = loadmat(stream, struct_as_record=False)
a20 = d['arr'][0,0]
assert_equal(a20.f1, 0.5)
assert_equal(a20.f2, 'python')
d = loadmat(stream, struct_as_record=True)
a20 = d['arr'][0,0]
assert_equal(a20['f1'], 0.5)
assert_equal(a20['f2'], 'python')
# structs always come back as object types
assert_equal(a20.dtype, np.dtype([('f1', 'O'),
('f2', 'O')]))
a21 = d['arr'].flat[1]
assert_equal(a21['f1'], 99)
assert_equal(a21['f2'], 'not perl')
def test_save_object():
class C(object):
pass
c = C()
c.field1 = 1
c.field2 = 'a string'
stream = BytesIO()
savemat(stream, {'c': c})
d = loadmat(stream, struct_as_record=False)
c2 = d['c'][0,0]
assert_equal(c2.field1, 1)
assert_equal(c2.field2, 'a string')
d = loadmat(stream, struct_as_record=True)
c2 = d['c'][0,0]
assert_equal(c2['field1'], 1)
assert_equal(c2['field2'], 'a string')
def test_read_opts():
# tests if read is seeing option sets, at initialization and after
# initialization
arr = np.arange(6).reshape(1,6)
stream = BytesIO()
savemat(stream, {'a': arr})
rdr = MatFile5Reader(stream)
back_dict = rdr.get_variables()
rarr = back_dict['a']
assert_array_equal(rarr, arr)
rdr = MatFile5Reader(stream, squeeze_me=True)
assert_array_equal(rdr.get_variables()['a'], arr.reshape((6,)))
rdr.squeeze_me = False
assert_array_equal(rarr, arr)
rdr = MatFile5Reader(stream, byte_order=boc.native_code)
assert_array_equal(rdr.get_variables()['a'], arr)
# inverted byte code leads to error on read because of swapped
# header etc
rdr = MatFile5Reader(stream, byte_order=boc.swapped_code)
assert_raises(Exception, rdr.get_variables)
rdr.byte_order = boc.native_code
assert_array_equal(rdr.get_variables()['a'], arr)
arr = np.array(['a string'])
stream.truncate(0)
stream.seek(0)
savemat(stream, {'a': arr})
rdr = MatFile5Reader(stream)
assert_array_equal(rdr.get_variables()['a'], arr)
rdr = MatFile5Reader(stream, chars_as_strings=False)
carr = np.atleast_2d(np.array(list(arr.item()), dtype='U1'))
assert_array_equal(rdr.get_variables()['a'], carr)
rdr.chars_as_strings = True
assert_array_equal(rdr.get_variables()['a'], arr)
def test_empty_string():
# make sure reading empty string does not raise error
estring_fname = pjoin(test_data_path, 'single_empty_string.mat')
fp = open(estring_fname, 'rb')
rdr = MatFile5Reader(fp)
d = rdr.get_variables()
fp.close()
assert_array_equal(d['a'], np.array([], dtype='U1'))
# empty string round trip. Matlab cannot distiguish
# between a string array that is empty, and a string array
# containing a single empty string, because it stores strings as
# arrays of char. There is no way of having an array of char that
# is not empty, but contains an empty string.
stream = BytesIO()
savemat(stream, {'a': np.array([''])})
rdr = MatFile5Reader(stream)
d = rdr.get_variables()
assert_array_equal(d['a'], np.array([], dtype='U1'))
stream.truncate(0)
stream.seek(0)
savemat(stream, {'a': np.array([], dtype='U1')})
rdr = MatFile5Reader(stream)
d = rdr.get_variables()
assert_array_equal(d['a'], np.array([], dtype='U1'))
stream.close()
def test_corrupted_data():
import zlib
for exc, fname in [(ValueError, 'corrupted_zlib_data.mat'),
(zlib.error, 'corrupted_zlib_checksum.mat')]:
with open(pjoin(test_data_path, fname), 'rb') as fp:
rdr = MatFile5Reader(fp)
assert_raises(exc, rdr.get_variables)
def test_corrupted_data_check_can_be_disabled():
with open(pjoin(test_data_path, 'corrupted_zlib_data.mat'), 'rb') as fp:
rdr = MatFile5Reader(fp, verify_compressed_data_integrity=False)
rdr.get_variables()
def test_read_both_endian():
# make sure big- and little- endian data is read correctly
for fname in ('big_endian.mat', 'little_endian.mat'):
fp = open(pjoin(test_data_path, fname), 'rb')
rdr = MatFile5Reader(fp)
d = rdr.get_variables()
fp.close()
assert_array_equal(d['strings'],
np.array([['hello'],
['world']], dtype=object))
assert_array_equal(d['floats'],
np.array([[2., 3.],
[3., 4.]], dtype=np.float32))
def test_write_opposite_endian():
# We don't support writing opposite endian .mat files, but we need to behave
# correctly if the user supplies an other-endian numpy array to write out
float_arr = np.array([[2., 3.],
[3., 4.]])
int_arr = np.arange(6).reshape((2, 3))
uni_arr = np.array(['hello', 'world'], dtype='U')
stream = BytesIO()
savemat(stream, {'floats': float_arr.byteswap().newbyteorder(),
'ints': int_arr.byteswap().newbyteorder(),
'uni_arr': uni_arr.byteswap().newbyteorder()})
rdr = MatFile5Reader(stream)
d = rdr.get_variables()
assert_array_equal(d['floats'], float_arr)
assert_array_equal(d['ints'], int_arr)
assert_array_equal(d['uni_arr'], uni_arr)
stream.close()
def test_logical_array():
# The roundtrip test doesn't verify that we load the data up with the
# correct (bool) dtype
with open(pjoin(test_data_path, 'testbool_8_WIN64.mat'), 'rb') as fobj:
rdr = MatFile5Reader(fobj, mat_dtype=True)
d = rdr.get_variables()
x = np.array([[True], [False]], dtype=np.bool_)
assert_array_equal(d['testbools'], x)
assert_equal(d['testbools'].dtype, x.dtype)
def test_logical_out_type():
# Confirm that bool type written as uint8, uint8 class
# See gh-4022
stream = BytesIO()
barr = np.array([False, True, False])
savemat(stream, {'barray': barr})
stream.seek(0)
reader = MatFile5Reader(stream)
reader.initialize_read()
reader.read_file_header()
hdr, _ = reader.read_var_header()
assert_equal(hdr.mclass, mio5p.mxUINT8_CLASS)
assert_equal(hdr.is_logical, True)
var = reader.read_var_array(hdr, False)
assert_equal(var.dtype.type, np.uint8)
def test_mat4_3d():
# test behavior when writing 3D arrays to matlab 4 files
stream = BytesIO()
arr = np.arange(24).reshape((2,3,4))
assert_raises(ValueError, savemat, stream, {'a': arr}, True, '4')
def test_func_read():
func_eg = pjoin(test_data_path, 'testfunc_7.4_GLNX86.mat')
fp = open(func_eg, 'rb')
rdr = MatFile5Reader(fp)
d = rdr.get_variables()
fp.close()
assert_(isinstance(d['testfunc'], MatlabFunction))
stream = BytesIO()
wtr = MatFile5Writer(stream)
assert_raises(MatWriteError, wtr.put_variables, d)
def test_mat_dtype():
double_eg = pjoin(test_data_path, 'testmatrix_6.1_SOL2.mat')
fp = open(double_eg, 'rb')
rdr = MatFile5Reader(fp, mat_dtype=False)
d = rdr.get_variables()
fp.close()
assert_equal(d['testmatrix'].dtype.kind, 'u')
fp = open(double_eg, 'rb')
rdr = MatFile5Reader(fp, mat_dtype=True)
d = rdr.get_variables()
fp.close()
assert_equal(d['testmatrix'].dtype.kind, 'f')
def test_sparse_in_struct():
# reproduces bug found by DC where Cython code was insisting on
# ndarray return type, but getting sparse matrix
st = {'sparsefield': SP.coo_matrix(np.eye(4))}
stream = BytesIO()
savemat(stream, {'a':st})
d = loadmat(stream, struct_as_record=True)
assert_array_equal(d['a'][0,0]['sparsefield'].todense(), np.eye(4))
def test_mat_struct_squeeze():
stream = BytesIO()
in_d = {'st':{'one':1, 'two':2}}
savemat(stream, in_d)
# no error without squeeze
out_d = loadmat(stream, struct_as_record=False)
# previous error was with squeeze, with mat_struct
out_d = loadmat(stream,
struct_as_record=False,
squeeze_me=True,
)
def test_scalar_squeeze():
stream = BytesIO()
in_d = {'scalar': [[0.1]], 'string': 'my name', 'st':{'one':1, 'two':2}}
savemat(stream, in_d)
out_d = loadmat(stream, squeeze_me=True)
assert_(isinstance(out_d['scalar'], float))
assert_(isinstance(out_d['string'], string_types))
assert_(isinstance(out_d['st'], np.ndarray))
def test_str_round():
# from report by Angus McMorland on mailing list 3 May 2010
stream = BytesIO()
in_arr = np.array(['Hello', 'Foob'])
out_arr = np.array(['Hello', 'Foob '])
savemat(stream, dict(a=in_arr))
res = loadmat(stream)
# resulted in ['HloolFoa', 'elWrdobr']
assert_array_equal(res['a'], out_arr)
stream.truncate(0)
stream.seek(0)
# Make Fortran ordered version of string
in_str = in_arr.tostring(order='F')
in_from_str = np.ndarray(shape=a.shape,
dtype=in_arr.dtype,
order='F',
buffer=in_str)
savemat(stream, dict(a=in_from_str))
assert_array_equal(res['a'], out_arr)
# unicode save did lead to buffer too small error
stream.truncate(0)
stream.seek(0)
in_arr_u = in_arr.astype('U')
out_arr_u = out_arr.astype('U')
savemat(stream, {'a': in_arr_u})
res = loadmat(stream)
assert_array_equal(res['a'], out_arr_u)
def test_fieldnames():
# Check that field names are as expected
stream = BytesIO()
savemat(stream, {'a': {'a':1, 'b':2}})
res = loadmat(stream)
field_names = res['a'].dtype.names
assert_equal(set(field_names), set(('a', 'b')))
def test_loadmat_varnames():
# Test that we can get just one variable from a mat file using loadmat
mat5_sys_names = ['__globals__',
'__header__',
'__version__']
for eg_file, sys_v_names in (
(pjoin(test_data_path, 'testmulti_4.2c_SOL2.mat'), []), (pjoin(
test_data_path, 'testmulti_7.4_GLNX86.mat'), mat5_sys_names)):
vars = loadmat(eg_file)
assert_equal(set(vars.keys()), set(['a', 'theta'] + sys_v_names))
vars = loadmat(eg_file, variable_names='a')
assert_equal(set(vars.keys()), set(['a'] + sys_v_names))
vars = loadmat(eg_file, variable_names=['a'])
assert_equal(set(vars.keys()), set(['a'] + sys_v_names))
vars = loadmat(eg_file, variable_names=['theta'])
assert_equal(set(vars.keys()), set(['theta'] + sys_v_names))
vars = loadmat(eg_file, variable_names=('theta',))
assert_equal(set(vars.keys()), set(['theta'] + sys_v_names))
vars = loadmat(eg_file, variable_names=[])
assert_equal(set(vars.keys()), set(sys_v_names))
vnames = ['theta']
vars = loadmat(eg_file, variable_names=vnames)
assert_equal(vnames, ['theta'])
def test_round_types():
# Check that saving, loading preserves dtype in most cases
arr = np.arange(10)
stream = BytesIO()
for dts in ('f8','f4','i8','i4','i2','i1',
'u8','u4','u2','u1','c16','c8'):
stream.truncate(0)
stream.seek(0) # needed for BytesIO in python 3
savemat(stream, {'arr': arr.astype(dts)})
vars = loadmat(stream)
assert_equal(np.dtype(dts), vars['arr'].dtype)
def test_varmats_from_mat():
# Make a mat file with several variables, write it, read it back
names_vars = (('arr', mlarr(np.arange(10))),
('mystr', mlarr('a string')),
('mynum', mlarr(10)))
# Dict like thing to give variables in defined order
class C(object):
def items(self):
return names_vars
stream = BytesIO()
savemat(stream, C())
varmats = varmats_from_mat(stream)
assert_equal(len(varmats), 3)
for i in range(3):
name, var_stream = varmats[i]
exp_name, exp_res = names_vars[i]
assert_equal(name, exp_name)
res = loadmat(var_stream)
assert_array_equal(res[name], exp_res)
def test_one_by_zero():
# Test 1x0 chars get read correctly
func_eg = pjoin(test_data_path, 'one_by_zero_char.mat')
fp = open(func_eg, 'rb')
rdr = MatFile5Reader(fp)
d = rdr.get_variables()
fp.close()
assert_equal(d['var'].shape, (0,))
def test_load_mat4_le():
# We were getting byte order wrong when reading little-endian floa64 dense
# matrices on big-endian platforms
mat4_fname = pjoin(test_data_path, 'test_mat4_le_floats.mat')
vars = loadmat(mat4_fname)
assert_array_equal(vars['a'], [[0.1, 1.2]])
def test_unicode_mat4():
# Mat4 should save unicode as latin1
bio = BytesIO()
var = {'second_cat': u('Schrödinger')}
savemat(bio, var, format='4')
var_back = loadmat(bio)
assert_equal(var_back['second_cat'], var['second_cat'])
def test_logical_sparse():
# Test we can read logical sparse stored in mat file as bytes.
# See https://github.com/scipy/scipy/issues/3539.
# In some files saved by MATLAB, the sparse data elements (Real Part
# Subelement in MATLAB speak) are stored with apparent type double
# (miDOUBLE) but are in fact single bytes.
filename = pjoin(test_data_path,'logical_sparse.mat')
# Before fix, this would crash with:
# ValueError: indices and data should have the same size
d = loadmat(filename, struct_as_record=True)
log_sp = d['sp_log_5_4']
assert_(isinstance(log_sp, SP.csc_matrix))
assert_equal(log_sp.dtype.type, np.bool_)
assert_array_equal(log_sp.toarray(),
[[True, True, True, False],
[False, False, True, False],
[False, False, True, False],
[False, False, False, False],
[False, False, False, False]])
def test_empty_sparse():
# Can we read empty sparse matrices?
sio = BytesIO()
import scipy.sparse
empty_sparse = scipy.sparse.csr_matrix([[0,0],[0,0]])
savemat(sio, dict(x=empty_sparse))
sio.seek(0)
res = loadmat(sio)
assert_array_equal(res['x'].shape, empty_sparse.shape)
assert_array_equal(res['x'].todense(), 0)
# Do empty sparse matrices get written with max nnz 1?
# See https://github.com/scipy/scipy/issues/4208
sio.seek(0)
reader = MatFile5Reader(sio)
reader.initialize_read()
reader.read_file_header()
hdr, _ = reader.read_var_header()
assert_equal(hdr.nzmax, 1)
def test_empty_mat_error():
# Test we get a specific warning for an empty mat file
sio = BytesIO()
assert_raises(MatReadError, loadmat, sio)
def test_miuint32_compromise():
# Reader should accept miUINT32 for miINT32, but check signs
# mat file with miUINT32 for miINT32, but OK values
filename = pjoin(test_data_path, 'miuint32_for_miint32.mat')
res = loadmat(filename)
assert_equal(res['an_array'], np.arange(10)[None, :])
# mat file with miUINT32 for miINT32, with negative value
filename = pjoin(test_data_path, 'bad_miuint32.mat')
with suppress_warnings() as sup:
sup.filter(message="unclosed file") # Py3k ResourceWarning
assert_raises(ValueError, loadmat, filename)
def test_miutf8_for_miint8_compromise():
# Check reader accepts ascii as miUTF8 for array names
filename = pjoin(test_data_path, 'miutf8_array_name.mat')
res = loadmat(filename)
assert_equal(res['array_name'], [[1]])
# mat file with non-ascii utf8 name raises error
filename = pjoin(test_data_path, 'bad_miutf8_array_name.mat')
with suppress_warnings() as sup:
sup.filter(message="unclosed file") # Py3k ResourceWarning
assert_raises(ValueError, loadmat, filename)
def test_bad_utf8():
# Check that reader reads bad UTF with 'replace' option
filename = pjoin(test_data_path,'broken_utf8.mat')
res = loadmat(filename)
assert_equal(res['bad_string'],
b'\x80 am broken'.decode('utf8', 'replace'))
def test_save_unicode_field(tmpdir):
filename = os.path.join(str(tmpdir), 'test.mat')
test_dict = {u'a':{u'b':1,u'c':'test_str'}}
savemat(filename, test_dict)
def test_filenotfound():
# Check the correct error is thrown
assert_raises(IOError, loadmat, "NotExistentFile00.mat")
assert_raises(IOError, loadmat, "NotExistentFile00")
| 42,289 | 33.132365 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/test_pathological.py
|
""" Test reading of files not conforming to matlab specification
We try and read any file that matlab reads, these files included
"""
from __future__ import division, print_function, absolute_import
from os.path import dirname, join as pjoin
from numpy.testing import assert_
from pytest import raises as assert_raises
from scipy.io.matlab.mio import loadmat
TEST_DATA_PATH = pjoin(dirname(__file__), 'data')
def test_multiple_fieldnames():
# Example provided by Dharhas Pothina
# Extracted using mio5.varmats_from_mat
multi_fname = pjoin(TEST_DATA_PATH, 'nasty_duplicate_fieldnames.mat')
vars = loadmat(multi_fname)
funny_names = vars['Summary'].dtype.names
assert_(set(['_1_Station_Q', '_2_Station_Q',
'_3_Station_Q']).issubset(funny_names))
def test_malformed1():
# Example from gh-6072
# Contains malformed header data, which previously resulted into a
# buffer overflow.
#
# Should raise an exception, not segfault
fname = pjoin(TEST_DATA_PATH, 'malformed1.mat')
with open(fname, 'rb') as f:
assert_raises(ValueError, loadmat, f)
| 1,125 | 30.277778 | 73 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/matlab/tests/gen_mat4files.m
|
% Generates mat files for loadmat unit tests
% Uses save_matfile.m function
% This is the version for matlab 4
% work out matlab version and file suffix for test files
global FILEPREFIX FILESUFFIX
sepchar = '/';
if strcmp(computer, 'PCWIN'), sepchar = '\'; end
FILEPREFIX = [pwd sepchar 'data' sepchar];
mlv = version;
FILESUFFIX = ['_' mlv '_' computer '.mat'];
% basic double array
theta = 0:pi/4:2*pi;
save_matfile('testdouble', theta);
% string
save_matfile('teststring', '"Do nine men interpret?" "Nine men," I nod.')
% complex
save_matfile('testcomplex', cos(theta) + 1j*sin(theta));
% asymmetric array to check indexing
a = zeros(3, 5);
a(:,1) = [1:3]';
a(1,:) = 1:5;
% 2D matrix
save_matfile('testmatrix', a);
% minus number - tests signed int
save_matfile('testminus', -1);
% single character
save_matfile('testonechar', 'r');
% string array
save_matfile('teststringarray', ['one '; 'two '; 'three']);
% sparse array
save_matfile('testsparse', sparse(a));
% sparse complex array
b = sparse(a);
b(1,1) = b(1,1) + j;
save_matfile('testsparsecomplex', b);
% Two variables in same file
save([FILEPREFIX 'testmulti' FILESUFFIX], 'a', 'theta')
| 1,163 | 21.823529 | 73 |
m
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/harwell_boeing/setup.py
|
from __future__ import division, print_function, absolute_import
def configuration(parent_package='',top_path=None):
from numpy.distutils.misc_util import Configuration
config = Configuration('harwell_boeing',parent_package,top_path)
config.add_data_dir('tests')
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())
| 417 | 26.866667 | 68 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/harwell_boeing/hb.py
|
"""
Implementation of Harwell-Boeing read/write.
At the moment not the full Harwell-Boeing format is supported. Supported
features are:
- assembled, non-symmetric, real matrices
- integer for pointer/indices
- exponential format for float values, and int format
"""
from __future__ import division, print_function, absolute_import
# TODO:
# - Add more support (symmetric/complex matrices, non-assembled matrices ?)
# XXX: reading is reasonably efficient (>= 85 % is in numpy.fromstring), but
# takes a lot of memory. Being faster would require compiled code.
# write is not efficient. Although not a terribly exciting task,
# having reusable facilities to efficiently read/write fortran-formatted files
# would be useful outside this module.
import warnings
import numpy as np
from scipy.sparse import csc_matrix
from scipy.io.harwell_boeing._fortran_format_parser import \
FortranFormatParser, IntFormat, ExpFormat
from scipy._lib.six import string_types
__all__ = ["MalformedHeader", "hb_read", "hb_write", "HBInfo", "HBFile",
"HBMatrixType"]
class MalformedHeader(Exception):
pass
class LineOverflow(Warning):
pass
def _nbytes_full(fmt, nlines):
"""Return the number of bytes to read to get every full lines for the
given parsed fortran format."""
return (fmt.repeat * fmt.width + 1) * (nlines - 1)
class HBInfo(object):
@classmethod
def from_data(cls, m, title="Default title", key="0", mxtype=None, fmt=None):
"""Create a HBInfo instance from an existing sparse matrix.
Parameters
----------
m : sparse matrix
the HBInfo instance will derive its parameters from m
title : str
Title to put in the HB header
key : str
Key
mxtype : HBMatrixType
type of the input matrix
fmt : dict
not implemented
Returns
-------
hb_info : HBInfo instance
"""
pointer = m.indptr
indices = m.indices
values = m.data
nrows, ncols = m.shape
nnon_zeros = m.nnz
if fmt is None:
# +1 because HB use one-based indexing (Fortran), and we will write
# the indices /pointer as such
pointer_fmt = IntFormat.from_number(np.max(pointer+1))
indices_fmt = IntFormat.from_number(np.max(indices+1))
if values.dtype.kind in np.typecodes["AllFloat"]:
values_fmt = ExpFormat.from_number(-np.max(np.abs(values)))
elif values.dtype.kind in np.typecodes["AllInteger"]:
values_fmt = IntFormat.from_number(-np.max(np.abs(values)))
else:
raise NotImplementedError("type %s not implemented yet" % values.dtype.kind)
else:
raise NotImplementedError("fmt argument not supported yet.")
if mxtype is None:
if not np.isrealobj(values):
raise ValueError("Complex values not supported yet")
if values.dtype.kind in np.typecodes["AllInteger"]:
tp = "integer"
elif values.dtype.kind in np.typecodes["AllFloat"]:
tp = "real"
else:
raise NotImplementedError("type %s for values not implemented"
% values.dtype)
mxtype = HBMatrixType(tp, "unsymmetric", "assembled")
else:
raise ValueError("mxtype argument not handled yet.")
def _nlines(fmt, size):
nlines = size // fmt.repeat
if nlines * fmt.repeat != size:
nlines += 1
return nlines
pointer_nlines = _nlines(pointer_fmt, pointer.size)
indices_nlines = _nlines(indices_fmt, indices.size)
values_nlines = _nlines(values_fmt, values.size)
total_nlines = pointer_nlines + indices_nlines + values_nlines
return cls(title, key,
total_nlines, pointer_nlines, indices_nlines, values_nlines,
mxtype, nrows, ncols, nnon_zeros,
pointer_fmt.fortran_format, indices_fmt.fortran_format,
values_fmt.fortran_format)
@classmethod
def from_file(cls, fid):
"""Create a HBInfo instance from a file object containing a matrix in the
HB format.
Parameters
----------
fid : file-like matrix
File or file-like object containing a matrix in the HB format.
Returns
-------
hb_info : HBInfo instance
"""
# First line
line = fid.readline().strip("\n")
if not len(line) > 72:
raise ValueError("Expected at least 72 characters for first line, "
"got: \n%s" % line)
title = line[:72]
key = line[72:]
# Second line
line = fid.readline().strip("\n")
if not len(line.rstrip()) >= 56:
raise ValueError("Expected at least 56 characters for second line, "
"got: \n%s" % line)
total_nlines = _expect_int(line[:14])
pointer_nlines = _expect_int(line[14:28])
indices_nlines = _expect_int(line[28:42])
values_nlines = _expect_int(line[42:56])
rhs_nlines = line[56:72].strip()
if rhs_nlines == '':
rhs_nlines = 0
else:
rhs_nlines = _expect_int(rhs_nlines)
if not rhs_nlines == 0:
raise ValueError("Only files without right hand side supported for "
"now.")
# Third line
line = fid.readline().strip("\n")
if not len(line) >= 70:
raise ValueError("Expected at least 72 character for third line, got:\n"
"%s" % line)
mxtype_s = line[:3].upper()
if not len(mxtype_s) == 3:
raise ValueError("mxtype expected to be 3 characters long")
mxtype = HBMatrixType.from_fortran(mxtype_s)
if mxtype.value_type not in ["real", "integer"]:
raise ValueError("Only real or integer matrices supported for "
"now (detected %s)" % mxtype)
if not mxtype.structure == "unsymmetric":
raise ValueError("Only unsymmetric matrices supported for "
"now (detected %s)" % mxtype)
if not mxtype.storage == "assembled":
raise ValueError("Only assembled matrices supported for now")
if not line[3:14] == " " * 11:
raise ValueError("Malformed data for third line: %s" % line)
nrows = _expect_int(line[14:28])
ncols = _expect_int(line[28:42])
nnon_zeros = _expect_int(line[42:56])
nelementals = _expect_int(line[56:70])
if not nelementals == 0:
raise ValueError("Unexpected value %d for nltvl (last entry of line 3)"
% nelementals)
# Fourth line
line = fid.readline().strip("\n")
ct = line.split()
if not len(ct) == 3:
raise ValueError("Expected 3 formats, got %s" % ct)
return cls(title, key,
total_nlines, pointer_nlines, indices_nlines, values_nlines,
mxtype, nrows, ncols, nnon_zeros,
ct[0], ct[1], ct[2],
rhs_nlines, nelementals)
def __init__(self, title, key,
total_nlines, pointer_nlines, indices_nlines, values_nlines,
mxtype, nrows, ncols, nnon_zeros,
pointer_format_str, indices_format_str, values_format_str,
right_hand_sides_nlines=0, nelementals=0):
"""Do not use this directly, but the class ctrs (from_* functions)."""
self.title = title
self.key = key
if title is None:
title = "No Title"
if len(title) > 72:
raise ValueError("title cannot be > 72 characters")
if key is None:
key = "|No Key"
if len(key) > 8:
warnings.warn("key is > 8 characters (key is %s)" % key, LineOverflow)
self.total_nlines = total_nlines
self.pointer_nlines = pointer_nlines
self.indices_nlines = indices_nlines
self.values_nlines = values_nlines
parser = FortranFormatParser()
pointer_format = parser.parse(pointer_format_str)
if not isinstance(pointer_format, IntFormat):
raise ValueError("Expected int format for pointer format, got %s"
% pointer_format)
indices_format = parser.parse(indices_format_str)
if not isinstance(indices_format, IntFormat):
raise ValueError("Expected int format for indices format, got %s" %
indices_format)
values_format = parser.parse(values_format_str)
if isinstance(values_format, ExpFormat):
if mxtype.value_type not in ["real", "complex"]:
raise ValueError("Inconsistency between matrix type %s and "
"value type %s" % (mxtype, values_format))
values_dtype = np.float64
elif isinstance(values_format, IntFormat):
if mxtype.value_type not in ["integer"]:
raise ValueError("Inconsistency between matrix type %s and "
"value type %s" % (mxtype, values_format))
# XXX: fortran int -> dtype association ?
values_dtype = int
else:
raise ValueError("Unsupported format for values %r" % (values_format,))
self.pointer_format = pointer_format
self.indices_format = indices_format
self.values_format = values_format
self.pointer_dtype = np.int32
self.indices_dtype = np.int32
self.values_dtype = values_dtype
self.pointer_nlines = pointer_nlines
self.pointer_nbytes_full = _nbytes_full(pointer_format, pointer_nlines)
self.indices_nlines = indices_nlines
self.indices_nbytes_full = _nbytes_full(indices_format, indices_nlines)
self.values_nlines = values_nlines
self.values_nbytes_full = _nbytes_full(values_format, values_nlines)
self.nrows = nrows
self.ncols = ncols
self.nnon_zeros = nnon_zeros
self.nelementals = nelementals
self.mxtype = mxtype
def dump(self):
"""Gives the header corresponding to this instance as a string."""
header = [self.title.ljust(72) + self.key.ljust(8)]
header.append("%14d%14d%14d%14d" %
(self.total_nlines, self.pointer_nlines,
self.indices_nlines, self.values_nlines))
header.append("%14s%14d%14d%14d%14d" %
(self.mxtype.fortran_format.ljust(14), self.nrows,
self.ncols, self.nnon_zeros, 0))
pffmt = self.pointer_format.fortran_format
iffmt = self.indices_format.fortran_format
vffmt = self.values_format.fortran_format
header.append("%16s%16s%20s" %
(pffmt.ljust(16), iffmt.ljust(16), vffmt.ljust(20)))
return "\n".join(header)
def _expect_int(value, msg=None):
try:
return int(value)
except ValueError:
if msg is None:
msg = "Expected an int, got %s"
raise ValueError(msg % value)
def _read_hb_data(content, header):
# XXX: look at a way to reduce memory here (big string creation)
ptr_string = "".join([content.read(header.pointer_nbytes_full),
content.readline()])
ptr = np.fromstring(ptr_string,
dtype=int, sep=' ')
ind_string = "".join([content.read(header.indices_nbytes_full),
content.readline()])
ind = np.fromstring(ind_string,
dtype=int, sep=' ')
val_string = "".join([content.read(header.values_nbytes_full),
content.readline()])
val = np.fromstring(val_string,
dtype=header.values_dtype, sep=' ')
try:
return csc_matrix((val, ind-1, ptr-1),
shape=(header.nrows, header.ncols))
except ValueError as e:
raise e
def _write_data(m, fid, header):
def write_array(f, ar, nlines, fmt):
# ar_nlines is the number of full lines, n is the number of items per
# line, ffmt the fortran format
pyfmt = fmt.python_format
pyfmt_full = pyfmt * fmt.repeat
# for each array to write, we first write the full lines, and special
# case for partial line
full = ar[:(nlines - 1) * fmt.repeat]
for row in full.reshape((nlines-1, fmt.repeat)):
f.write(pyfmt_full % tuple(row) + "\n")
nremain = ar.size - full.size
if nremain > 0:
f.write((pyfmt * nremain) % tuple(ar[ar.size - nremain:]) + "\n")
fid.write(header.dump())
fid.write("\n")
# +1 is for fortran one-based indexing
write_array(fid, m.indptr+1, header.pointer_nlines,
header.pointer_format)
write_array(fid, m.indices+1, header.indices_nlines,
header.indices_format)
write_array(fid, m.data, header.values_nlines,
header.values_format)
class HBMatrixType(object):
"""Class to hold the matrix type."""
# q2f* translates qualified names to fortran character
_q2f_type = {
"real": "R",
"complex": "C",
"pattern": "P",
"integer": "I",
}
_q2f_structure = {
"symmetric": "S",
"unsymmetric": "U",
"hermitian": "H",
"skewsymmetric": "Z",
"rectangular": "R"
}
_q2f_storage = {
"assembled": "A",
"elemental": "E",
}
_f2q_type = dict([(j, i) for i, j in _q2f_type.items()])
_f2q_structure = dict([(j, i) for i, j in _q2f_structure.items()])
_f2q_storage = dict([(j, i) for i, j in _q2f_storage.items()])
@classmethod
def from_fortran(cls, fmt):
if not len(fmt) == 3:
raise ValueError("Fortran format for matrix type should be 3 "
"characters long")
try:
value_type = cls._f2q_type[fmt[0]]
structure = cls._f2q_structure[fmt[1]]
storage = cls._f2q_storage[fmt[2]]
return cls(value_type, structure, storage)
except KeyError:
raise ValueError("Unrecognized format %s" % fmt)
def __init__(self, value_type, structure, storage="assembled"):
self.value_type = value_type
self.structure = structure
self.storage = storage
if value_type not in self._q2f_type:
raise ValueError("Unrecognized type %s" % value_type)
if structure not in self._q2f_structure:
raise ValueError("Unrecognized structure %s" % structure)
if storage not in self._q2f_storage:
raise ValueError("Unrecognized storage %s" % storage)
@property
def fortran_format(self):
return self._q2f_type[self.value_type] + \
self._q2f_structure[self.structure] + \
self._q2f_storage[self.storage]
def __repr__(self):
return "HBMatrixType(%s, %s, %s)" % \
(self.value_type, self.structure, self.storage)
class HBFile(object):
def __init__(self, file, hb_info=None):
"""Create a HBFile instance.
Parameters
----------
file : file-object
StringIO work as well
hb_info : HBInfo, optional
Should be given as an argument for writing, in which case the file
should be writable.
"""
self._fid = file
if hb_info is None:
self._hb_info = HBInfo.from_file(file)
else:
#raise IOError("file %s is not writable, and hb_info "
# "was given." % file)
self._hb_info = hb_info
@property
def title(self):
return self._hb_info.title
@property
def key(self):
return self._hb_info.key
@property
def type(self):
return self._hb_info.mxtype.value_type
@property
def structure(self):
return self._hb_info.mxtype.structure
@property
def storage(self):
return self._hb_info.mxtype.storage
def read_matrix(self):
return _read_hb_data(self._fid, self._hb_info)
def write_matrix(self, m):
return _write_data(m, self._fid, self._hb_info)
def hb_read(path_or_open_file):
"""Read HB-format file.
Parameters
----------
path_or_open_file : path-like or file-like
If a file-like object, it is used as-is. Otherwise it is opened
before reading.
Returns
-------
data : scipy.sparse.csc_matrix instance
The data read from the HB file as a sparse matrix.
Notes
-----
At the moment not the full Harwell-Boeing format is supported. Supported
features are:
- assembled, non-symmetric, real matrices
- integer for pointer/indices
- exponential format for float values, and int format
"""
def _get_matrix(fid):
hb = HBFile(fid)
return hb.read_matrix()
if hasattr(path_or_open_file, 'read'):
return _get_matrix(path_or_open_file)
else:
with open(path_or_open_file) as f:
return _get_matrix(f)
def hb_write(path_or_open_file, m, hb_info=None):
"""Write HB-format file.
Parameters
----------
path_or_open_file : path-like or file-like
If a file-like object, it is used as-is. Otherwise it is opened
before writing.
m : sparse-matrix
the sparse matrix to write
hb_info : HBInfo
contains the meta-data for write
Returns
-------
None
Notes
-----
At the moment not the full Harwell-Boeing format is supported. Supported
features are:
- assembled, non-symmetric, real matrices
- integer for pointer/indices
- exponential format for float values, and int format
"""
if hb_info is None:
hb_info = HBInfo.from_data(m)
def _set_matrix(fid):
hb = HBFile(fid, hb_info)
return hb.write_matrix(m)
if hasattr(path_or_open_file, 'write'):
return _set_matrix(path_or_open_file)
else:
with open(path_or_open_file, 'w') as f:
return _set_matrix(f)
| 18,422 | 32.865809 | 92 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/harwell_boeing/_fortran_format_parser.py
|
"""
Preliminary module to handle fortran formats for IO. Does not use this outside
scipy.sparse io for now, until the API is deemed reasonable.
The *Format classes handle conversion between fortran and python format, and
FortranFormatParser can create *Format instances from raw fortran format
strings (e.g. '(3I4)', '(10I3)', etc...)
"""
from __future__ import division, print_function, absolute_import
import re
import warnings
import numpy as np
__all__ = ["BadFortranFormat", "FortranFormatParser", "IntFormat", "ExpFormat"]
TOKENS = {
"LPAR": r"\(",
"RPAR": r"\)",
"INT_ID": r"I",
"EXP_ID": r"E",
"INT": r"\d+",
"DOT": r"\.",
}
class BadFortranFormat(SyntaxError):
pass
def number_digits(n):
return int(np.floor(np.log10(np.abs(n))) + 1)
class IntFormat(object):
@classmethod
def from_number(cls, n, min=None):
"""Given an integer, returns a "reasonable" IntFormat instance to represent
any number between 0 and n if n > 0, -n and n if n < 0
Parameters
----------
n : int
max number one wants to be able to represent
min : int
minimum number of characters to use for the format
Returns
-------
res : IntFormat
IntFormat instance with reasonable (see Notes) computed width
Notes
-----
Reasonable should be understood as the minimal string length necessary
without losing precision. For example, IntFormat.from_number(1) will
return an IntFormat instance of width 2, so that any 0 and 1 may be
represented as 1-character strings without loss of information.
"""
width = number_digits(n) + 1
if n < 0:
width += 1
repeat = 80 // width
return cls(width, min, repeat=repeat)
def __init__(self, width, min=None, repeat=None):
self.width = width
self.repeat = repeat
self.min = min
def __repr__(self):
r = "IntFormat("
if self.repeat:
r += "%d" % self.repeat
r += "I%d" % self.width
if self.min:
r += ".%d" % self.min
return r + ")"
@property
def fortran_format(self):
r = "("
if self.repeat:
r += "%d" % self.repeat
r += "I%d" % self.width
if self.min:
r += ".%d" % self.min
return r + ")"
@property
def python_format(self):
return "%" + str(self.width) + "d"
class ExpFormat(object):
@classmethod
def from_number(cls, n, min=None):
"""Given a float number, returns a "reasonable" ExpFormat instance to
represent any number between -n and n.
Parameters
----------
n : float
max number one wants to be able to represent
min : int
minimum number of characters to use for the format
Returns
-------
res : ExpFormat
ExpFormat instance with reasonable (see Notes) computed width
Notes
-----
Reasonable should be understood as the minimal string length necessary
to avoid losing precision.
"""
# len of one number in exp format: sign + 1|0 + "." +
# number of digit for fractional part + 'E' + sign of exponent +
# len of exponent
finfo = np.finfo(n.dtype)
# Number of digits for fractional part
n_prec = finfo.precision + 1
# Number of digits for exponential part
n_exp = number_digits(np.max(np.abs([finfo.maxexp, finfo.minexp])))
width = 1 + 1 + n_prec + 1 + n_exp + 1
if n < 0:
width += 1
repeat = int(np.floor(80 / width))
return cls(width, n_prec, min, repeat=repeat)
def __init__(self, width, significand, min=None, repeat=None):
"""\
Parameters
----------
width : int
number of characters taken by the string (includes space).
"""
self.width = width
self.significand = significand
self.repeat = repeat
self.min = min
def __repr__(self):
r = "ExpFormat("
if self.repeat:
r += "%d" % self.repeat
r += "E%d.%d" % (self.width, self.significand)
if self.min:
r += "E%d" % self.min
return r + ")"
@property
def fortran_format(self):
r = "("
if self.repeat:
r += "%d" % self.repeat
r += "E%d.%d" % (self.width, self.significand)
if self.min:
r += "E%d" % self.min
return r + ")"
@property
def python_format(self):
return "%" + str(self.width-1) + "." + str(self.significand) + "E"
class Token(object):
def __init__(self, type, value, pos):
self.type = type
self.value = value
self.pos = pos
def __str__(self):
return """Token('%s', "%s")""" % (self.type, self.value)
def __repr__(self):
return self.__str__()
class Tokenizer(object):
def __init__(self):
self.tokens = list(TOKENS.keys())
self.res = [re.compile(TOKENS[i]) for i in self.tokens]
def input(self, s):
self.data = s
self.curpos = 0
self.len = len(s)
def next_token(self):
curpos = self.curpos
tokens = self.tokens
while curpos < self.len:
for i, r in enumerate(self.res):
m = r.match(self.data, curpos)
if m is None:
continue
else:
self.curpos = m.end()
return Token(self.tokens[i], m.group(), self.curpos)
raise SyntaxError("Unknown character at position %d (%s)"
% (self.curpos, self.data[curpos]))
# Grammar for fortran format:
# format : LPAR format_string RPAR
# format_string : repeated | simple
# repeated : repeat simple
# simple : int_fmt | exp_fmt
# int_fmt : INT_ID width
# exp_fmt : simple_exp_fmt
# simple_exp_fmt : EXP_ID width DOT significand
# extended_exp_fmt : EXP_ID width DOT significand EXP_ID ndigits
# repeat : INT
# width : INT
# significand : INT
# ndigits : INT
# Naive fortran formatter - parser is hand-made
class FortranFormatParser(object):
"""Parser for fortran format strings. The parse method returns a *Format
instance.
Notes
-----
Only ExpFormat (exponential format for floating values) and IntFormat
(integer format) for now.
"""
def __init__(self):
self.tokenizer = Tokenizer()
def parse(self, s):
self.tokenizer.input(s)
tokens = []
try:
while True:
t = self.tokenizer.next_token()
if t is None:
break
else:
tokens.append(t)
return self._parse_format(tokens)
except SyntaxError as e:
raise BadFortranFormat(str(e))
def _get_min(self, tokens):
next = tokens.pop(0)
if not next.type == "DOT":
raise SyntaxError()
next = tokens.pop(0)
return next.value
def _expect(self, token, tp):
if not token.type == tp:
raise SyntaxError()
def _parse_format(self, tokens):
if not tokens[0].type == "LPAR":
raise SyntaxError("Expected left parenthesis at position "
"%d (got '%s')" % (0, tokens[0].value))
elif not tokens[-1].type == "RPAR":
raise SyntaxError("Expected right parenthesis at position "
"%d (got '%s')" % (len(tokens), tokens[-1].value))
tokens = tokens[1:-1]
types = [t.type for t in tokens]
if types[0] == "INT":
repeat = int(tokens.pop(0).value)
else:
repeat = None
next = tokens.pop(0)
if next.type == "INT_ID":
next = self._next(tokens, "INT")
width = int(next.value)
if tokens:
min = int(self._get_min(tokens))
else:
min = None
return IntFormat(width, min, repeat)
elif next.type == "EXP_ID":
next = self._next(tokens, "INT")
width = int(next.value)
next = self._next(tokens, "DOT")
next = self._next(tokens, "INT")
significand = int(next.value)
if tokens:
next = self._next(tokens, "EXP_ID")
next = self._next(tokens, "INT")
min = int(next.value)
else:
min = None
return ExpFormat(width, significand, min, repeat)
else:
raise SyntaxError("Invalid formater type %s" % next.value)
def _next(self, tokens, tp):
if not len(tokens) > 0:
raise SyntaxError()
next = tokens.pop(0)
self._expect(next, tp)
return next
| 9,066 | 27.875796 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/harwell_boeing/__init__.py
|
from __future__ import division, print_function, absolute_import
from scipy.io.harwell_boeing.hb import MalformedHeader, HBInfo, HBFile, \
HBMatrixType, hb_read, hb_write
| 176 | 34.4 | 73 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/harwell_boeing/tests/test_fortran_format.py
|
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import assert_equal
from pytest import raises as assert_raises
from scipy.io.harwell_boeing._fortran_format_parser import (
FortranFormatParser, IntFormat, ExpFormat, BadFortranFormat,
number_digits)
class TestFortranFormatParser(object):
def setup_method(self):
self.parser = FortranFormatParser()
def _test_equal(self, format, ref):
ret = self.parser.parse(format)
assert_equal(ret.__dict__, ref.__dict__)
def test_simple_int(self):
self._test_equal("(I4)", IntFormat(4))
def test_simple_repeated_int(self):
self._test_equal("(3I4)", IntFormat(4, repeat=3))
def test_simple_exp(self):
self._test_equal("(E4.3)", ExpFormat(4, 3))
def test_exp_exp(self):
self._test_equal("(E8.3E3)", ExpFormat(8, 3, 3))
def test_repeat_exp(self):
self._test_equal("(2E4.3)", ExpFormat(4, 3, repeat=2))
def test_repeat_exp_exp(self):
self._test_equal("(2E8.3E3)", ExpFormat(8, 3, 3, repeat=2))
def test_wrong_formats(self):
def _test_invalid(bad_format):
assert_raises(BadFortranFormat, lambda: self.parser.parse(bad_format))
_test_invalid("I4")
_test_invalid("(E4)")
_test_invalid("(E4.)")
_test_invalid("(E4.E3)")
class TestIntFormat(object):
def test_to_fortran(self):
f = [IntFormat(10), IntFormat(12, 10), IntFormat(12, 10, 3)]
res = ["(I10)", "(I12.10)", "(3I12.10)"]
for i, j in zip(f, res):
assert_equal(i.fortran_format, j)
def test_from_number(self):
f = [10, -12, 123456789]
r_f = [IntFormat(3, repeat=26), IntFormat(4, repeat=20),
IntFormat(10, repeat=8)]
for i, j in zip(f, r_f):
assert_equal(IntFormat.from_number(i).__dict__, j.__dict__)
class TestExpFormat(object):
def test_to_fortran(self):
f = [ExpFormat(10, 5), ExpFormat(12, 10), ExpFormat(12, 10, min=3),
ExpFormat(10, 5, repeat=3)]
res = ["(E10.5)", "(E12.10)", "(E12.10E3)", "(3E10.5)"]
for i, j in zip(f, res):
assert_equal(i.fortran_format, j)
def test_from_number(self):
f = np.array([1.0, -1.2])
r_f = [ExpFormat(24, 16, repeat=3), ExpFormat(25, 16, repeat=3)]
for i, j in zip(f, r_f):
assert_equal(ExpFormat.from_number(i).__dict__, j.__dict__)
| 2,495 | 31 | 82 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/harwell_boeing/tests/test_hb.py
|
from __future__ import division, print_function, absolute_import
import os
import sys
if sys.version_info[0] >= 3:
from io import StringIO
else:
from StringIO import StringIO
import tempfile
import numpy as np
from numpy.testing import assert_equal, \
assert_array_almost_equal_nulp
from scipy.sparse import coo_matrix, csc_matrix, rand
from scipy.io import hb_read, hb_write
from scipy.io.harwell_boeing import HBFile, HBInfo
SIMPLE = """\
No Title |No Key
9 4 1 4
RUA 100 100 10 0
(26I3) (26I3) (3E23.15)
1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 4 4 4 6 6 6 6 6 6 6 6 6 6 6 8 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 11
37 71 89 18 30 45 70 19 25 52
2.971243799687726e-01 3.662366682877375e-01 4.786962174699534e-01
6.490068647991184e-01 6.617490424831662e-02 8.870370343191623e-01
4.196478590163001e-01 5.649603072111251e-01 9.934423887087086e-01
6.912334991524289e-01
"""
SIMPLE_MATRIX = coo_matrix(
(
(0.297124379969, 0.366236668288, 0.47869621747, 0.649006864799,
0.0661749042483, 0.887037034319, 0.419647859016,
0.564960307211, 0.993442388709, 0.691233499152,),
(np.array([[36, 70, 88, 17, 29, 44, 69, 18, 24, 51],
[0, 4, 58, 61, 61, 72, 72, 73, 99, 99]]))))
def assert_csc_almost_equal(r, l):
r = csc_matrix(r)
l = csc_matrix(l)
assert_equal(r.indptr, l.indptr)
assert_equal(r.indices, l.indices)
assert_array_almost_equal_nulp(r.data, l.data, 10000)
class TestHBReader(object):
def test_simple(self):
m = hb_read(StringIO(SIMPLE))
assert_csc_almost_equal(m, SIMPLE_MATRIX)
class TestRBRoundtrip(object):
def test_simple(self):
rm = rand(100, 1000, 0.05).tocsc()
fd, filename = tempfile.mkstemp(suffix="rb")
try:
hb_write(filename, rm, HBInfo.from_data(rm))
m = hb_read(filename)
finally:
os.close(fd)
os.remove(filename)
assert_csc_almost_equal(m, rm)
| 2,375 | 31.547945 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/harwell_boeing/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/arff/arffread.py
|
# Last Change: Mon Aug 20 08:00 PM 2007 J
from __future__ import division, print_function, absolute_import
import re
import itertools
import datetime
from functools import partial
import numpy as np
from scipy._lib.six import next
"""A module to read arff files."""
__all__ = ['MetaData', 'loadarff', 'ArffError', 'ParseArffError']
# An Arff file is basically two parts:
# - header
# - data
#
# A header has each of its components starting by @META where META is one of
# the keyword (attribute of relation, for now).
# TODO:
# - both integer and reals are treated as numeric -> the integer info
# is lost!
# - Replace ValueError by ParseError or something
# We know can handle the following:
# - numeric and nominal attributes
# - missing values for numeric attributes
r_meta = re.compile(r'^\s*@')
# Match a comment
r_comment = re.compile(r'^%')
# Match an empty line
r_empty = re.compile(r'^\s+$')
# Match a header line, that is a line which starts by @ + a word
r_headerline = re.compile(r'^@\S*')
r_datameta = re.compile(r'^@[Dd][Aa][Tt][Aa]')
r_relation = re.compile(r'^@[Rr][Ee][Ll][Aa][Tt][Ii][Oo][Nn]\s*(\S*)')
r_attribute = re.compile(r'^@[Aa][Tt][Tt][Rr][Ii][Bb][Uu][Tt][Ee]\s*(..*$)')
# To get attributes name enclosed with ''
r_comattrval = re.compile(r"'(..+)'\s+(..+$)")
# To get normal attributes
r_wcomattrval = re.compile(r"(\S+)\s+(..+$)")
#-------------------------
# Module defined exception
#-------------------------
class ArffError(IOError):
pass
class ParseArffError(ArffError):
pass
#------------------
# Various utilities
#------------------
# An attribute is defined as @attribute name value
def parse_type(attrtype):
"""Given an arff attribute value (meta data), returns its type.
Expect the value to be a name."""
uattribute = attrtype.lower().strip()
if uattribute[0] == '{':
return 'nominal'
elif uattribute[:len('real')] == 'real':
return 'numeric'
elif uattribute[:len('integer')] == 'integer':
return 'numeric'
elif uattribute[:len('numeric')] == 'numeric':
return 'numeric'
elif uattribute[:len('string')] == 'string':
return 'string'
elif uattribute[:len('relational')] == 'relational':
return 'relational'
elif uattribute[:len('date')] == 'date':
return 'date'
else:
raise ParseArffError("unknown attribute %s" % uattribute)
def get_nominal(attribute):
"""If attribute is nominal, returns a list of the values"""
return attribute.split(',')
def read_data_list(ofile):
"""Read each line of the iterable and put it in a list."""
data = [next(ofile)]
if data[0].strip()[0] == '{':
raise ValueError("This looks like a sparse ARFF: not supported yet")
data.extend([i for i in ofile])
return data
def get_ndata(ofile):
"""Read the whole file to get number of data attributes."""
data = [next(ofile)]
loc = 1
if data[0].strip()[0] == '{':
raise ValueError("This looks like a sparse ARFF: not supported yet")
for i in ofile:
loc += 1
return loc
def maxnomlen(atrv):
"""Given a string containing a nominal type definition, returns the
string len of the biggest component.
A nominal type is defined as seomthing framed between brace ({}).
Parameters
----------
atrv : str
Nominal type definition
Returns
-------
slen : int
length of longest component
Examples
--------
maxnomlen("{floup, bouga, fl, ratata}") returns 6 (the size of
ratata, the longest nominal value).
>>> maxnomlen("{floup, bouga, fl, ratata}")
6
"""
nomtp = get_nom_val(atrv)
return max(len(i) for i in nomtp)
def get_nom_val(atrv):
"""Given a string containing a nominal type, returns a tuple of the
possible values.
A nominal type is defined as something framed between braces ({}).
Parameters
----------
atrv : str
Nominal type definition
Returns
-------
poss_vals : tuple
possible values
Examples
--------
>>> get_nom_val("{floup, bouga, fl, ratata}")
('floup', 'bouga', 'fl', 'ratata')
"""
r_nominal = re.compile('{(.+)}')
m = r_nominal.match(atrv)
if m:
return tuple(i.strip() for i in m.group(1).split(','))
else:
raise ValueError("This does not look like a nominal string")
def get_date_format(atrv):
r_date = re.compile(r"[Dd][Aa][Tt][Ee]\s+[\"']?(.+?)[\"']?$")
m = r_date.match(atrv)
if m:
pattern = m.group(1).strip()
# convert time pattern from Java's SimpleDateFormat to C's format
datetime_unit = None
if "yyyy" in pattern:
pattern = pattern.replace("yyyy", "%Y")
datetime_unit = "Y"
elif "yy":
pattern = pattern.replace("yy", "%y")
datetime_unit = "Y"
if "MM" in pattern:
pattern = pattern.replace("MM", "%m")
datetime_unit = "M"
if "dd" in pattern:
pattern = pattern.replace("dd", "%d")
datetime_unit = "D"
if "HH" in pattern:
pattern = pattern.replace("HH", "%H")
datetime_unit = "h"
if "mm" in pattern:
pattern = pattern.replace("mm", "%M")
datetime_unit = "m"
if "ss" in pattern:
pattern = pattern.replace("ss", "%S")
datetime_unit = "s"
if "z" in pattern or "Z" in pattern:
raise ValueError("Date type attributes with time zone not "
"supported, yet")
if datetime_unit is None:
raise ValueError("Invalid or unsupported date format")
return pattern, datetime_unit
else:
raise ValueError("Invalid or no date format")
def go_data(ofile):
"""Skip header.
the first next() call of the returned iterator will be the @data line"""
return itertools.dropwhile(lambda x: not r_datameta.match(x), ofile)
#----------------
# Parsing header
#----------------
def tokenize_attribute(iterable, attribute):
"""Parse a raw string in header (eg starts by @attribute).
Given a raw string attribute, try to get the name and type of the
attribute. Constraints:
* The first line must start with @attribute (case insensitive, and
space like characters before @attribute are allowed)
* Works also if the attribute is spread on multilines.
* Works if empty lines or comments are in between
Parameters
----------
attribute : str
the attribute string.
Returns
-------
name : str
name of the attribute
value : str
value of the attribute
next : str
next line to be parsed
Examples
--------
If attribute is a string defined in python as r"floupi real", will
return floupi as name, and real as value.
>>> iterable = iter([0] * 10) # dummy iterator
>>> tokenize_attribute(iterable, r"@attribute floupi real")
('floupi', 'real', 0)
If attribute is r"'floupi 2' real", will return 'floupi 2' as name,
and real as value.
>>> tokenize_attribute(iterable, r" @attribute 'floupi 2' real ")
('floupi 2', 'real', 0)
"""
sattr = attribute.strip()
mattr = r_attribute.match(sattr)
if mattr:
# atrv is everything after @attribute
atrv = mattr.group(1)
if r_comattrval.match(atrv):
name, type = tokenize_single_comma(atrv)
next_item = next(iterable)
elif r_wcomattrval.match(atrv):
name, type = tokenize_single_wcomma(atrv)
next_item = next(iterable)
else:
# Not sure we should support this, as it does not seem supported by
# weka.
raise ValueError("multi line not supported yet")
#name, type, next_item = tokenize_multilines(iterable, atrv)
else:
raise ValueError("First line unparsable: %s" % sattr)
if type == 'relational':
raise ValueError("relational attributes not supported yet")
return name, type, next_item
def tokenize_single_comma(val):
# XXX we match twice the same string (here and at the caller level). It is
# stupid, but it is easier for now...
m = r_comattrval.match(val)
if m:
try:
name = m.group(1).strip()
type = m.group(2).strip()
except IndexError:
raise ValueError("Error while tokenizing attribute")
else:
raise ValueError("Error while tokenizing single %s" % val)
return name, type
def tokenize_single_wcomma(val):
# XXX we match twice the same string (here and at the caller level). It is
# stupid, but it is easier for now...
m = r_wcomattrval.match(val)
if m:
try:
name = m.group(1).strip()
type = m.group(2).strip()
except IndexError:
raise ValueError("Error while tokenizing attribute")
else:
raise ValueError("Error while tokenizing single %s" % val)
return name, type
def read_header(ofile):
"""Read the header of the iterable ofile."""
i = next(ofile)
# Pass first comments
while r_comment.match(i):
i = next(ofile)
# Header is everything up to DATA attribute ?
relation = None
attributes = []
while not r_datameta.match(i):
m = r_headerline.match(i)
if m:
isattr = r_attribute.match(i)
if isattr:
name, type, i = tokenize_attribute(ofile, i)
attributes.append((name, type))
else:
isrel = r_relation.match(i)
if isrel:
relation = isrel.group(1)
else:
raise ValueError("Error parsing line %s" % i)
i = next(ofile)
else:
i = next(ofile)
return relation, attributes
#--------------------
# Parsing actual data
#--------------------
def safe_float(x):
"""given a string x, convert it to a float. If the stripped string is a ?,
return a Nan (missing value).
Parameters
----------
x : str
string to convert
Returns
-------
f : float
where float can be nan
Examples
--------
>>> safe_float('1')
1.0
>>> safe_float('1\\n')
1.0
>>> safe_float('?\\n')
nan
"""
if '?' in x:
return np.nan
else:
return float(x)
def safe_nominal(value, pvalue):
svalue = value.strip()
if svalue in pvalue:
return svalue
elif svalue == '?':
return svalue
else:
raise ValueError("%s value not in %s" % (str(svalue), str(pvalue)))
def safe_date(value, date_format, datetime_unit):
date_str = value.strip().strip("'").strip('"')
if date_str == '?':
return np.datetime64('NaT', datetime_unit)
else:
dt = datetime.datetime.strptime(date_str, date_format)
return np.datetime64(dt).astype("datetime64[%s]" % datetime_unit)
class MetaData(object):
"""Small container to keep useful information on a ARFF dataset.
Knows about attributes names and types.
Examples
--------
::
data, meta = loadarff('iris.arff')
# This will print the attributes names of the iris.arff dataset
for i in meta:
print(i)
# This works too
meta.names()
# Getting attribute type
types = meta.types()
Notes
-----
Also maintains the list of attributes in order, i.e. doing for i in
meta, where meta is an instance of MetaData, will return the
different attribute names in the order they were defined.
"""
def __init__(self, rel, attr):
self.name = rel
# We need the dictionary to be ordered
# XXX: may be better to implement an ordered dictionary
self._attributes = {}
self._attrnames = []
for name, value in attr:
tp = parse_type(value)
self._attrnames.append(name)
if tp == 'nominal':
self._attributes[name] = (tp, get_nom_val(value))
elif tp == 'date':
self._attributes[name] = (tp, get_date_format(value)[0])
else:
self._attributes[name] = (tp, None)
def __repr__(self):
msg = ""
msg += "Dataset: %s\n" % self.name
for i in self._attrnames:
msg += "\t%s's type is %s" % (i, self._attributes[i][0])
if self._attributes[i][1]:
msg += ", range is %s" % str(self._attributes[i][1])
msg += '\n'
return msg
def __iter__(self):
return iter(self._attrnames)
def __getitem__(self, key):
return self._attributes[key]
def names(self):
"""Return the list of attribute names."""
return self._attrnames
def types(self):
"""Return the list of attribute types."""
attr_types = [self._attributes[name][0] for name in self._attrnames]
return attr_types
def loadarff(f):
"""
Read an arff file.
The data is returned as a record array, which can be accessed much like
a dictionary of numpy arrays. For example, if one of the attributes is
called 'pressure', then its first 10 data points can be accessed from the
``data`` record array like so: ``data['pressure'][0:10]``
Parameters
----------
f : file-like or str
File-like object to read from, or filename to open.
Returns
-------
data : record array
The data of the arff file, accessible by attribute names.
meta : `MetaData`
Contains information about the arff file such as name and
type of attributes, the relation (name of the dataset), etc...
Raises
------
ParseArffError
This is raised if the given file is not ARFF-formatted.
NotImplementedError
The ARFF file has an attribute which is not supported yet.
Notes
-----
This function should be able to read most arff files. Not
implemented functionality include:
* date type attributes
* string type attributes
It can read files with numeric and nominal attributes. It cannot read
files with sparse data ({} in the file). However, this function can
read files with missing data (? in the file), representing the data
points as NaNs.
Examples
--------
>>> from scipy.io import arff
>>> from io import StringIO
>>> content = \"\"\"
... @relation foo
... @attribute width numeric
... @attribute height numeric
... @attribute color {red,green,blue,yellow,black}
... @data
... 5.0,3.25,blue
... 4.5,3.75,green
... 3.0,4.00,red
... \"\"\"
>>> f = StringIO(content)
>>> data, meta = arff.loadarff(f)
>>> data
array([(5.0, 3.25, 'blue'), (4.5, 3.75, 'green'), (3.0, 4.0, 'red')],
dtype=[('width', '<f8'), ('height', '<f8'), ('color', '|S6')])
>>> meta
Dataset: foo
\twidth's type is numeric
\theight's type is numeric
\tcolor's type is nominal, range is ('red', 'green', 'blue', 'yellow', 'black')
"""
if hasattr(f, 'read'):
ofile = f
else:
ofile = open(f, 'rt')
try:
return _loadarff(ofile)
finally:
if ofile is not f: # only close what we opened
ofile.close()
def _loadarff(ofile):
# Parse the header file
try:
rel, attr = read_header(ofile)
except ValueError as e:
msg = "Error while parsing header, error was: " + str(e)
raise ParseArffError(msg)
# Check whether we have a string attribute (not supported yet)
hasstr = False
for name, value in attr:
type = parse_type(value)
if type == 'string':
hasstr = True
meta = MetaData(rel, attr)
# XXX The following code is not great
# Build the type descriptor descr and the list of convertors to convert
# each attribute to the suitable type (which should match the one in
# descr).
# This can be used once we want to support integer as integer values and
# not as numeric anymore (using masked arrays ?).
acls2dtype = {'real': float, 'integer': float, 'numeric': float}
acls2conv = {'real': safe_float,
'integer': safe_float,
'numeric': safe_float}
descr = []
convertors = []
if not hasstr:
for name, value in attr:
type = parse_type(value)
if type == 'date':
date_format, datetime_unit = get_date_format(value)
descr.append((name, "datetime64[%s]" % datetime_unit))
convertors.append(partial(safe_date, date_format=date_format,
datetime_unit=datetime_unit))
elif type == 'nominal':
n = maxnomlen(value)
descr.append((name, 'S%d' % n))
pvalue = get_nom_val(value)
convertors.append(partial(safe_nominal, pvalue=pvalue))
else:
descr.append((name, acls2dtype[type]))
convertors.append(safe_float)
#dc.append(acls2conv[type])
#sdescr.append((name, acls2sdtype[type]))
else:
# How to support string efficiently ? Ideally, we should know the max
# size of the string before allocating the numpy array.
raise NotImplementedError("String attributes not supported yet, sorry")
ni = len(convertors)
def generator(row_iter, delim=','):
# TODO: this is where we are spending times (~80%). I think things
# could be made more efficiently:
# - We could for example "compile" the function, because some values
# do not change here.
# - The function to convert a line to dtyped values could also be
# generated on the fly from a string and be executed instead of
# looping.
# - The regex are overkill: for comments, checking that a line starts
# by % should be enough and faster, and for empty lines, same thing
# --> this does not seem to change anything.
# 'compiling' the range since it does not change
# Note, I have already tried zipping the converters and
# row elements and got slightly worse performance.
elems = list(range(ni))
for raw in row_iter:
# We do not abstract skipping comments and empty lines for
# performance reasons.
if r_comment.match(raw) or r_empty.match(raw):
continue
row = raw.split(delim)
yield tuple([convertors[i](row[i]) for i in elems])
a = generator(ofile)
# No error should happen here: it is a bug otherwise
data = np.fromiter(a, descr)
return data, meta
#-----
# Misc
#-----
def basic_stats(data):
nbfac = data.size * 1. / (data.size - 1)
return np.nanmin(data), np.nanmax(data), np.mean(data), np.std(data) * nbfac
def print_attribute(name, tp, data):
type = tp[0]
if type == 'numeric' or type == 'real' or type == 'integer':
min, max, mean, std = basic_stats(data)
print("%s,%s,%f,%f,%f,%f" % (name, type, min, max, mean, std))
else:
msg = name + ",{"
for i in range(len(tp[1])-1):
msg += tp[1][i] + ","
msg += tp[1][-1]
msg += "}"
print(msg)
def test_weka(filename):
data, meta = loadarff(filename)
print(len(data.dtype))
print(data.size)
for i in meta:
print_attribute(i, meta[i], data[i])
# make sure nose does not find this as a test
test_weka.__test__ = False
if __name__ == '__main__':
import sys
filename = sys.argv[1]
test_weka(filename)
| 19,810 | 28.52459 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/arff/setup.py
|
from __future__ import division, print_function, absolute_import
def configuration(parent_package='io',top_path=None):
from numpy.distutils.misc_util import Configuration
config = Configuration('arff', parent_package, top_path)
config.add_data_dir('tests')
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())
| 410 | 28.357143 | 64 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/arff/__init__.py
|
"""
Module to read ARFF files, which are the standard data format for WEKA.
ARFF is a text file format which support numerical, string and data values.
The format can also represent missing data and sparse data.
Notes
-----
The ARFF support in ``scipy.io`` provides file reading functionality only.
For more extensive ARFF functionality, see `liac-arff
<https://github.com/renatopp/liac-arff>`_.
See the `WEKA website <http://weka.wikispaces.com/ARFF>`_
for more details about the ARFF format and available datasets.
"""
from __future__ import division, print_function, absolute_import
from .arffread import *
from . import arffread
__all__ = arffread.__all__
from scipy._lib._testutils import PytestTester
test = PytestTester(__name__)
del PytestTester
| 761 | 27.222222 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/arff/tests/test_arffread.py
|
from __future__ import division, print_function, absolute_import
import datetime
import os
import sys
from os.path import join as pjoin
if sys.version_info[0] >= 3:
from io import StringIO
else:
from cStringIO import StringIO
import numpy as np
from numpy.testing import (assert_array_almost_equal,
assert_array_equal, assert_equal, assert_)
import pytest
from pytest import raises as assert_raises
from scipy.io.arff.arffread import loadarff
from scipy.io.arff.arffread import read_header, parse_type, ParseArffError
data_path = pjoin(os.path.dirname(__file__), 'data')
test1 = pjoin(data_path, 'test1.arff')
test2 = pjoin(data_path, 'test2.arff')
test3 = pjoin(data_path, 'test3.arff')
test4 = pjoin(data_path, 'test4.arff')
test5 = pjoin(data_path, 'test5.arff')
test6 = pjoin(data_path, 'test6.arff')
test7 = pjoin(data_path, 'test7.arff')
test8 = pjoin(data_path, 'test8.arff')
expect4_data = [(0.1, 0.2, 0.3, 0.4, 'class1'),
(-0.1, -0.2, -0.3, -0.4, 'class2'),
(1, 2, 3, 4, 'class3')]
expected_types = ['numeric', 'numeric', 'numeric', 'numeric', 'nominal']
missing = pjoin(data_path, 'missing.arff')
expect_missing_raw = np.array([[1, 5], [2, 4], [np.nan, np.nan]])
expect_missing = np.empty(3, [('yop', float), ('yap', float)])
expect_missing['yop'] = expect_missing_raw[:, 0]
expect_missing['yap'] = expect_missing_raw[:, 1]
class TestData(object):
def test1(self):
# Parsing trivial file with nothing.
self._test(test4)
def test2(self):
# Parsing trivial file with some comments in the data section.
self._test(test5)
def test3(self):
# Parsing trivial file with nominal attribute of 1 character.
self._test(test6)
def _test(self, test_file):
data, meta = loadarff(test_file)
for i in range(len(data)):
for j in range(4):
assert_array_almost_equal(expect4_data[i][j], data[i][j])
assert_equal(meta.types(), expected_types)
def test_filelike(self):
# Test reading from file-like object (StringIO)
f1 = open(test1)
data1, meta1 = loadarff(f1)
f1.close()
f2 = open(test1)
data2, meta2 = loadarff(StringIO(f2.read()))
f2.close()
assert_(data1 == data2)
assert_(repr(meta1) == repr(meta2))
@pytest.mark.skipif(sys.version_info < (3, 6),
reason='Passing path-like objects to IO functions requires Python >= 3.6')
def test_path(self):
# Test reading from `pathlib.Path` object
from pathlib import Path
with open(test1) as f1:
data1, meta1 = loadarff(f1)
data2, meta2 = loadarff(Path(test1))
assert_(data1 == data2)
assert_(repr(meta1) == repr(meta2))
class TestMissingData(object):
def test_missing(self):
data, meta = loadarff(missing)
for i in ['yop', 'yap']:
assert_array_almost_equal(data[i], expect_missing[i])
class TestNoData(object):
def test_nodata(self):
# The file nodata.arff has no data in the @DATA section.
# Reading it should result in an array with length 0.
nodata_filename = os.path.join(data_path, 'nodata.arff')
data, meta = loadarff(nodata_filename)
expected_dtype = np.dtype([('sepallength', '<f8'),
('sepalwidth', '<f8'),
('petallength', '<f8'),
('petalwidth', '<f8'),
('class', 'S15')])
assert_equal(data.dtype, expected_dtype)
assert_equal(data.size, 0)
class TestHeader(object):
def test_type_parsing(self):
# Test parsing type of attribute from their value.
ofile = open(test2)
rel, attrs = read_header(ofile)
ofile.close()
expected = ['numeric', 'numeric', 'numeric', 'numeric', 'numeric',
'numeric', 'string', 'string', 'nominal', 'nominal']
for i in range(len(attrs)):
assert_(parse_type(attrs[i][1]) == expected[i])
def test_badtype_parsing(self):
# Test parsing wrong type of attribute from their value.
ofile = open(test3)
rel, attrs = read_header(ofile)
ofile.close()
for name, value in attrs:
assert_raises(ParseArffError, parse_type, value)
def test_fullheader1(self):
# Parsing trivial header with nothing.
ofile = open(test1)
rel, attrs = read_header(ofile)
ofile.close()
# Test relation
assert_(rel == 'test1')
# Test numerical attributes
assert_(len(attrs) == 5)
for i in range(4):
assert_(attrs[i][0] == 'attr%d' % i)
assert_(attrs[i][1] == 'REAL')
# Test nominal attribute
assert_(attrs[4][0] == 'class')
assert_(attrs[4][1] == '{class0, class1, class2, class3}')
def test_dateheader(self):
ofile = open(test7)
rel, attrs = read_header(ofile)
ofile.close()
assert_(rel == 'test7')
assert_(len(attrs) == 5)
assert_(attrs[0][0] == 'attr_year')
assert_(attrs[0][1] == 'DATE yyyy')
assert_(attrs[1][0] == 'attr_month')
assert_(attrs[1][1] == 'DATE yyyy-MM')
assert_(attrs[2][0] == 'attr_date')
assert_(attrs[2][1] == 'DATE yyyy-MM-dd')
assert_(attrs[3][0] == 'attr_datetime_local')
assert_(attrs[3][1] == 'DATE "yyyy-MM-dd HH:mm"')
assert_(attrs[4][0] == 'attr_datetime_missing')
assert_(attrs[4][1] == 'DATE "yyyy-MM-dd HH:mm"')
def test_dateheader_unsupported(self):
ofile = open(test8)
rel, attrs = read_header(ofile)
ofile.close()
assert_(rel == 'test8')
assert_(len(attrs) == 2)
assert_(attrs[0][0] == 'attr_datetime_utc')
assert_(attrs[0][1] == 'DATE "yyyy-MM-dd HH:mm Z"')
assert_(attrs[1][0] == 'attr_datetime_full')
assert_(attrs[1][1] == 'DATE "yy-MM-dd HH:mm:ss z"')
class TestDateAttribute(object):
def setup_method(self):
self.data, self.meta = loadarff(test7)
def test_year_attribute(self):
expected = np.array([
'1999',
'2004',
'1817',
'2100',
'2013',
'1631'
], dtype='datetime64[Y]')
assert_array_equal(self.data["attr_year"], expected)
def test_month_attribute(self):
expected = np.array([
'1999-01',
'2004-12',
'1817-04',
'2100-09',
'2013-11',
'1631-10'
], dtype='datetime64[M]')
assert_array_equal(self.data["attr_month"], expected)
def test_date_attribute(self):
expected = np.array([
'1999-01-31',
'2004-12-01',
'1817-04-28',
'2100-09-10',
'2013-11-30',
'1631-10-15'
], dtype='datetime64[D]')
assert_array_equal(self.data["attr_date"], expected)
def test_datetime_local_attribute(self):
expected = np.array([
datetime.datetime(year=1999, month=1, day=31, hour=0, minute=1),
datetime.datetime(year=2004, month=12, day=1, hour=23, minute=59),
datetime.datetime(year=1817, month=4, day=28, hour=13, minute=0),
datetime.datetime(year=2100, month=9, day=10, hour=12, minute=0),
datetime.datetime(year=2013, month=11, day=30, hour=4, minute=55),
datetime.datetime(year=1631, month=10, day=15, hour=20, minute=4)
], dtype='datetime64[m]')
assert_array_equal(self.data["attr_datetime_local"], expected)
def test_datetime_missing(self):
expected = np.array([
'nat',
'2004-12-01T23:59',
'nat',
'nat',
'2013-11-30T04:55',
'1631-10-15T20:04'
], dtype='datetime64[m]')
assert_array_equal(self.data["attr_datetime_missing"], expected)
def test_datetime_timezone(self):
assert_raises(ValueError, loadarff, test8)
| 8,190 | 30.503846 | 98 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/arff/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/tests/test_paths.py
|
"""
Ensure that we can use pathlib.Path objects in all relevant IO functions.
"""
import sys
try:
from pathlib import Path
except ImportError:
# Not available. No fallback import, since we'll skip the entire
# test suite for Python < 3.6.
pass
import numpy as np
from numpy.testing import assert_
import pytest
import scipy.io
import scipy.io.wavfile
from scipy._lib._tmpdirs import tempdir
import scipy.sparse
@pytest.mark.skipif(sys.version_info < (3, 6),
reason='Passing path-like objects to IO functions requires Python >= 3.6')
class TestPaths(object):
data = np.arange(5).astype(np.int64)
def test_savemat(self):
with tempdir() as temp_dir:
path = Path(temp_dir) / 'data.mat'
scipy.io.savemat(path, {'data': self.data})
assert_(path.is_file())
def test_loadmat(self):
# Save data with string path, load with pathlib.Path
with tempdir() as temp_dir:
path = Path(temp_dir) / 'data.mat'
scipy.io.savemat(str(path), {'data': self.data})
mat_contents = scipy.io.loadmat(path)
assert_((mat_contents['data'] == self.data).all())
def test_whosmat(self):
# Save data with string path, load with pathlib.Path
with tempdir() as temp_dir:
path = Path(temp_dir) / 'data.mat'
scipy.io.savemat(str(path), {'data': self.data})
contents = scipy.io.whosmat(path)
assert_(contents[0] == ('data', (1, 5), 'int64'))
def test_readsav(self):
path = Path(__file__).parent / 'data/scalar_string.sav'
scipy.io.readsav(path)
def test_hb_read(self):
# Save data with string path, load with pathlib.Path
with tempdir() as temp_dir:
data = scipy.sparse.csr_matrix(scipy.sparse.eye(3))
path = Path(temp_dir) / 'data.hb'
scipy.io.harwell_boeing.hb_write(str(path), data)
data_new = scipy.io.harwell_boeing.hb_read(path)
assert_((data_new != data).nnz == 0)
def test_hb_write(self):
with tempdir() as temp_dir:
data = scipy.sparse.csr_matrix(scipy.sparse.eye(3))
path = Path(temp_dir) / 'data.hb'
scipy.io.harwell_boeing.hb_write(path, data)
assert_(path.is_file())
def test_netcdf_file(self):
path = Path(__file__).parent / 'data/example_1.nc'
scipy.io.netcdf.netcdf_file(path)
def test_wavfile_read(self):
path = Path(__file__).parent / 'data/test-8000Hz-le-2ch-1byteu.wav'
scipy.io.wavfile.read(path)
def test_wavfile_write(self):
# Read from str path, write to Path
input_path = Path(__file__).parent / 'data/test-8000Hz-le-2ch-1byteu.wav'
rate, data = scipy.io.wavfile.read(str(input_path))
with tempdir() as temp_dir:
output_path = Path(temp_dir) / input_path.name
scipy.io.wavfile.write(output_path, rate, data)
| 2,994 | 32.651685 | 94 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/tests/test_netcdf.py
|
''' Tests for netcdf '''
from __future__ import division, print_function, absolute_import
import os
from os.path import join as pjoin, dirname
import shutil
import tempfile
import warnings
from io import BytesIO
from glob import glob
from contextlib import contextmanager
import numpy as np
from numpy.testing import assert_, assert_allclose, assert_equal
from pytest import raises as assert_raises
from scipy.io.netcdf import netcdf_file, IS_PYPY
from scipy._lib._numpy_compat import suppress_warnings
from scipy._lib._tmpdirs import in_tempdir
TEST_DATA_PATH = pjoin(dirname(__file__), 'data')
N_EG_ELS = 11 # number of elements for example variable
VARTYPE_EG = 'b' # var type for example variable
@contextmanager
def make_simple(*args, **kwargs):
f = netcdf_file(*args, **kwargs)
f.history = 'Created for a test'
f.createDimension('time', N_EG_ELS)
time = f.createVariable('time', VARTYPE_EG, ('time',))
time[:] = np.arange(N_EG_ELS)
time.units = 'days since 2008-01-01'
f.flush()
yield f
f.close()
def check_simple(ncfileobj):
'''Example fileobj tests '''
assert_equal(ncfileobj.history, b'Created for a test')
time = ncfileobj.variables['time']
assert_equal(time.units, b'days since 2008-01-01')
assert_equal(time.shape, (N_EG_ELS,))
assert_equal(time[-1], N_EG_ELS-1)
def assert_mask_matches(arr, expected_mask):
'''
Asserts that the mask of arr is effectively the same as expected_mask.
In contrast to numpy.ma.testutils.assert_mask_equal, this function allows
testing the 'mask' of a standard numpy array (the mask in this case is treated
as all False).
Parameters
----------
arr: ndarray or MaskedArray
Array to test.
expected_mask: array_like of booleans
A list giving the expected mask.
'''
mask = np.ma.getmaskarray(arr)
assert_equal(mask, expected_mask)
def test_read_write_files():
# test round trip for example file
cwd = os.getcwd()
try:
tmpdir = tempfile.mkdtemp()
os.chdir(tmpdir)
with make_simple('simple.nc', 'w') as f:
pass
# read the file we just created in 'a' mode
with netcdf_file('simple.nc', 'a') as f:
check_simple(f)
# add something
f._attributes['appendRan'] = 1
# To read the NetCDF file we just created::
with netcdf_file('simple.nc') as f:
# Using mmap is the default (but not on pypy)
assert_equal(f.use_mmap, not IS_PYPY)
check_simple(f)
assert_equal(f._attributes['appendRan'], 1)
# Read it in append (and check mmap is off)
with netcdf_file('simple.nc', 'a') as f:
assert_(not f.use_mmap)
check_simple(f)
assert_equal(f._attributes['appendRan'], 1)
# Now without mmap
with netcdf_file('simple.nc', mmap=False) as f:
# Using mmap is the default
assert_(not f.use_mmap)
check_simple(f)
# To read the NetCDF file we just created, as file object, no
# mmap. When n * n_bytes(var_type) is not divisible by 4, this
# raised an error in pupynere 1.0.12 and scipy rev 5893, because
# calculated vsize was rounding up in units of 4 - see
# https://www.unidata.ucar.edu/software/netcdf/docs/user_guide.html
with open('simple.nc', 'rb') as fobj:
with netcdf_file(fobj) as f:
# by default, don't use mmap for file-like
assert_(not f.use_mmap)
check_simple(f)
# Read file from fileobj, with mmap
with suppress_warnings() as sup:
if IS_PYPY:
sup.filter(RuntimeWarning,
"Cannot close a netcdf_file opened with mmap=True.*")
with open('simple.nc', 'rb') as fobj:
with netcdf_file(fobj, mmap=True) as f:
assert_(f.use_mmap)
check_simple(f)
# Again read it in append mode (adding another att)
with open('simple.nc', 'r+b') as fobj:
with netcdf_file(fobj, 'a') as f:
assert_(not f.use_mmap)
check_simple(f)
f.createDimension('app_dim', 1)
var = f.createVariable('app_var', 'i', ('app_dim',))
var[:] = 42
# And... check that app_var made it in...
with netcdf_file('simple.nc') as f:
check_simple(f)
assert_equal(f.variables['app_var'][:], 42)
except:
os.chdir(cwd)
shutil.rmtree(tmpdir)
raise
os.chdir(cwd)
shutil.rmtree(tmpdir)
def test_read_write_sio():
eg_sio1 = BytesIO()
with make_simple(eg_sio1, 'w') as f1:
str_val = eg_sio1.getvalue()
eg_sio2 = BytesIO(str_val)
with netcdf_file(eg_sio2) as f2:
check_simple(f2)
# Test that error is raised if attempting mmap for sio
eg_sio3 = BytesIO(str_val)
assert_raises(ValueError, netcdf_file, eg_sio3, 'r', True)
# Test 64-bit offset write / read
eg_sio_64 = BytesIO()
with make_simple(eg_sio_64, 'w', version=2) as f_64:
str_val = eg_sio_64.getvalue()
eg_sio_64 = BytesIO(str_val)
with netcdf_file(eg_sio_64) as f_64:
check_simple(f_64)
assert_equal(f_64.version_byte, 2)
# also when version 2 explicitly specified
eg_sio_64 = BytesIO(str_val)
with netcdf_file(eg_sio_64, version=2) as f_64:
check_simple(f_64)
assert_equal(f_64.version_byte, 2)
def test_bytes():
raw_file = BytesIO()
f = netcdf_file(raw_file, mode='w')
# Dataset only has a single variable, dimension and attribute to avoid
# any ambiguity related to order.
f.a = 'b'
f.createDimension('dim', 1)
var = f.createVariable('var', np.int16, ('dim',))
var[0] = -9999
var.c = 'd'
f.sync()
actual = raw_file.getvalue()
expected = (b'CDF\x01'
b'\x00\x00\x00\x00'
b'\x00\x00\x00\x0a'
b'\x00\x00\x00\x01'
b'\x00\x00\x00\x03'
b'dim\x00'
b'\x00\x00\x00\x01'
b'\x00\x00\x00\x0c'
b'\x00\x00\x00\x01'
b'\x00\x00\x00\x01'
b'a\x00\x00\x00'
b'\x00\x00\x00\x02'
b'\x00\x00\x00\x01'
b'b\x00\x00\x00'
b'\x00\x00\x00\x0b'
b'\x00\x00\x00\x01'
b'\x00\x00\x00\x03'
b'var\x00'
b'\x00\x00\x00\x01'
b'\x00\x00\x00\x00'
b'\x00\x00\x00\x0c'
b'\x00\x00\x00\x01'
b'\x00\x00\x00\x01'
b'c\x00\x00\x00'
b'\x00\x00\x00\x02'
b'\x00\x00\x00\x01'
b'd\x00\x00\x00'
b'\x00\x00\x00\x03'
b'\x00\x00\x00\x04'
b'\x00\x00\x00\x78'
b'\xd8\xf1\x80\x01')
assert_equal(actual, expected)
def test_encoded_fill_value():
with netcdf_file(BytesIO(), mode='w') as f:
f.createDimension('x', 1)
var = f.createVariable('var', 'S1', ('x',))
assert_equal(var._get_encoded_fill_value(), b'\x00')
var._FillValue = b'\x01'
assert_equal(var._get_encoded_fill_value(), b'\x01')
var._FillValue = b'\x00\x00' # invalid, wrong size
assert_equal(var._get_encoded_fill_value(), b'\x00')
def test_read_example_data():
# read any example data files
for fname in glob(pjoin(TEST_DATA_PATH, '*.nc')):
with netcdf_file(fname, 'r') as f:
pass
with netcdf_file(fname, 'r', mmap=False) as f:
pass
def test_itemset_no_segfault_on_readonly():
# Regression test for ticket #1202.
# Open the test file in read-only mode.
filename = pjoin(TEST_DATA_PATH, 'example_1.nc')
with suppress_warnings() as sup:
sup.filter(RuntimeWarning,
"Cannot close a netcdf_file opened with mmap=True, when netcdf_variables or arrays referring to its data still exist")
with netcdf_file(filename, 'r', mmap=True) as f:
time_var = f.variables['time']
# time_var.assignValue(42) should raise a RuntimeError--not seg. fault!
assert_raises(RuntimeError, time_var.assignValue, 42)
def test_appending_issue_gh_8625():
stream = BytesIO()
with make_simple(stream, mode='w') as f:
f.createDimension('x', 2)
f.createVariable('x', float, ('x',))
f.variables['x'][...] = 1
f.flush()
contents = stream.getvalue()
stream = BytesIO(contents)
with netcdf_file(stream, mode='a') as f:
f.variables['x'][...] = 2
def test_write_invalid_dtype():
dtypes = ['int64', 'uint64']
if np.dtype('int').itemsize == 8: # 64-bit machines
dtypes.append('int')
if np.dtype('uint').itemsize == 8: # 64-bit machines
dtypes.append('uint')
with netcdf_file(BytesIO(), 'w') as f:
f.createDimension('time', N_EG_ELS)
for dt in dtypes:
assert_raises(ValueError, f.createVariable, 'time', dt, ('time',))
def test_flush_rewind():
stream = BytesIO()
with make_simple(stream, mode='w') as f:
x = f.createDimension('x',4)
v = f.createVariable('v', 'i2', ['x'])
v[:] = 1
f.flush()
len_single = len(stream.getvalue())
f.flush()
len_double = len(stream.getvalue())
assert_(len_single == len_double)
def test_dtype_specifiers():
# Numpy 1.7.0-dev had a bug where 'i2' wouldn't work.
# Specifying np.int16 or similar only works from the same commit as this
# comment was made.
with make_simple(BytesIO(), mode='w') as f:
f.createDimension('x',4)
f.createVariable('v1', 'i2', ['x'])
f.createVariable('v2', np.int16, ['x'])
f.createVariable('v3', np.dtype(np.int16), ['x'])
def test_ticket_1720():
io = BytesIO()
items = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]
with netcdf_file(io, 'w') as f:
f.history = 'Created for a test'
f.createDimension('float_var', 10)
float_var = f.createVariable('float_var', 'f', ('float_var',))
float_var[:] = items
float_var.units = 'metres'
f.flush()
contents = io.getvalue()
io = BytesIO(contents)
with netcdf_file(io, 'r') as f:
assert_equal(f.history, b'Created for a test')
float_var = f.variables['float_var']
assert_equal(float_var.units, b'metres')
assert_equal(float_var.shape, (10,))
assert_allclose(float_var[:], items)
def test_mmaps_segfault():
filename = pjoin(TEST_DATA_PATH, 'example_1.nc')
if not IS_PYPY:
with warnings.catch_warnings():
warnings.simplefilter("error")
with netcdf_file(filename, mmap=True) as f:
x = f.variables['lat'][:]
# should not raise warnings
del x
def doit():
with netcdf_file(filename, mmap=True) as f:
return f.variables['lat'][:]
# should not crash
with suppress_warnings() as sup:
sup.filter(RuntimeWarning,
"Cannot close a netcdf_file opened with mmap=True, when netcdf_variables or arrays referring to its data still exist")
x = doit()
x.sum()
def test_zero_dimensional_var():
io = BytesIO()
with make_simple(io, 'w') as f:
v = f.createVariable('zerodim', 'i2', [])
# This is checking that .isrec returns a boolean - don't simplify it
# to 'assert not ...'
assert v.isrec is False, v.isrec
f.flush()
def test_byte_gatts():
# Check that global "string" atts work like they did before py3k
# unicode and general bytes confusion
with in_tempdir():
filename = 'g_byte_atts.nc'
f = netcdf_file(filename, 'w')
f._attributes['holy'] = b'grail'
f._attributes['witch'] = 'floats'
f.close()
f = netcdf_file(filename, 'r')
assert_equal(f._attributes['holy'], b'grail')
assert_equal(f._attributes['witch'], b'floats')
f.close()
def test_open_append():
# open 'w' put one attr
with in_tempdir():
filename = 'append_dat.nc'
f = netcdf_file(filename, 'w')
f._attributes['Kilroy'] = 'was here'
f.close()
# open again in 'a', read the att and and a new one
f = netcdf_file(filename, 'a')
assert_equal(f._attributes['Kilroy'], b'was here')
f._attributes['naughty'] = b'Zoot'
f.close()
# open yet again in 'r' and check both atts
f = netcdf_file(filename, 'r')
assert_equal(f._attributes['Kilroy'], b'was here')
assert_equal(f._attributes['naughty'], b'Zoot')
f.close()
def test_append_recordDimension():
dataSize = 100
with in_tempdir():
# Create file with record time dimension
with netcdf_file('withRecordDimension.nc', 'w') as f:
f.createDimension('time', None)
f.createVariable('time', 'd', ('time',))
f.createDimension('x', dataSize)
x = f.createVariable('x', 'd', ('x',))
x[:] = np.array(range(dataSize))
f.createDimension('y', dataSize)
y = f.createVariable('y', 'd', ('y',))
y[:] = np.array(range(dataSize))
f.createVariable('testData', 'i', ('time', 'x', 'y'))
f.flush()
f.close()
for i in range(2):
# Open the file in append mode and add data
with netcdf_file('withRecordDimension.nc', 'a') as f:
f.variables['time'].data = np.append(f.variables["time"].data, i)
f.variables['testData'][i, :, :] = np.ones((dataSize, dataSize))*i
f.flush()
# Read the file and check that append worked
with netcdf_file('withRecordDimension.nc') as f:
assert_equal(f.variables['time'][-1], i)
assert_equal(f.variables['testData'][-1, :, :].copy(), np.ones((dataSize, dataSize))*i)
assert_equal(f.variables['time'].data.shape[0], i+1)
assert_equal(f.variables['testData'].data.shape[0], i+1)
# Read the file and check that 'data' was not saved as user defined
# attribute of testData variable during append operation
with netcdf_file('withRecordDimension.nc') as f:
with assert_raises(KeyError) as ar:
f.variables['testData']._attributes['data']
ex = ar.value
assert_equal(ex.args[0], 'data')
def test_maskandscale():
t = np.linspace(20, 30, 15)
t[3] = 100
tm = np.ma.masked_greater(t, 99)
fname = pjoin(TEST_DATA_PATH, 'example_2.nc')
with netcdf_file(fname, maskandscale=True) as f:
Temp = f.variables['Temperature']
assert_equal(Temp.missing_value, 9999)
assert_equal(Temp.add_offset, 20)
assert_equal(Temp.scale_factor, np.float32(0.01))
found = Temp[:].compressed()
del Temp # Remove ref to mmap, so file can be closed.
expected = np.round(tm.compressed(), 2)
assert_allclose(found, expected)
with in_tempdir():
newfname = 'ms.nc'
f = netcdf_file(newfname, 'w', maskandscale=True)
f.createDimension('Temperature', len(tm))
temp = f.createVariable('Temperature', 'i', ('Temperature',))
temp.missing_value = 9999
temp.scale_factor = 0.01
temp.add_offset = 20
temp[:] = tm
f.close()
with netcdf_file(newfname, maskandscale=True) as f:
Temp = f.variables['Temperature']
assert_equal(Temp.missing_value, 9999)
assert_equal(Temp.add_offset, 20)
assert_equal(Temp.scale_factor, np.float32(0.01))
expected = np.round(tm.compressed(), 2)
found = Temp[:].compressed()
del Temp
assert_allclose(found, expected)
# ------------------------------------------------------------------------
# Test reading with masked values (_FillValue / missing_value)
# ------------------------------------------------------------------------
def test_read_withValuesNearFillValue():
# Regression test for ticket #5626
fname = pjoin(TEST_DATA_PATH, 'example_3_maskedvals.nc')
with netcdf_file(fname, maskandscale=True) as f:
vardata = f.variables['var1_fillval0'][:]
assert_mask_matches(vardata, [False, True, False])
def test_read_withNoFillValue():
# For a variable with no fill value, reading data with maskandscale=True
# should return unmasked data
fname = pjoin(TEST_DATA_PATH, 'example_3_maskedvals.nc')
with netcdf_file(fname, maskandscale=True) as f:
vardata = f.variables['var2_noFillval'][:]
assert_mask_matches(vardata, [False, False, False])
assert_equal(vardata, [1,2,3])
def test_read_withFillValueAndMissingValue():
# For a variable with both _FillValue and missing_value, the _FillValue
# should be used
IRRELEVANT_VALUE = 9999
fname = pjoin(TEST_DATA_PATH, 'example_3_maskedvals.nc')
with netcdf_file(fname, maskandscale=True) as f:
vardata = f.variables['var3_fillvalAndMissingValue'][:]
assert_mask_matches(vardata, [True, False, False])
assert_equal(vardata, [IRRELEVANT_VALUE, 2, 3])
def test_read_withMissingValue():
# For a variable with missing_value but not _FillValue, the missing_value
# should be used
fname = pjoin(TEST_DATA_PATH, 'example_3_maskedvals.nc')
with netcdf_file(fname, maskandscale=True) as f:
vardata = f.variables['var4_missingValue'][:]
assert_mask_matches(vardata, [False, True, False])
def test_read_withFillValNaN():
fname = pjoin(TEST_DATA_PATH, 'example_3_maskedvals.nc')
with netcdf_file(fname, maskandscale=True) as f:
vardata = f.variables['var5_fillvalNaN'][:]
assert_mask_matches(vardata, [False, True, False])
def test_read_withChar():
fname = pjoin(TEST_DATA_PATH, 'example_3_maskedvals.nc')
with netcdf_file(fname, maskandscale=True) as f:
vardata = f.variables['var6_char'][:]
assert_mask_matches(vardata, [False, True, False])
def test_read_with2dVar():
fname = pjoin(TEST_DATA_PATH, 'example_3_maskedvals.nc')
with netcdf_file(fname, maskandscale=True) as f:
vardata = f.variables['var7_2d'][:]
assert_mask_matches(vardata, [[True, False], [False, False], [False, True]])
def test_read_withMaskAndScaleFalse():
# If a variable has a _FillValue (or missing_value) attribute, but is read
# with maskandscale set to False, the result should be unmasked
fname = pjoin(TEST_DATA_PATH, 'example_3_maskedvals.nc')
# Open file with mmap=False to avoid problems with closing a mmap'ed file
# when arrays referring to its data still exist:
with netcdf_file(fname, maskandscale=False, mmap=False) as f:
vardata = f.variables['var3_fillvalAndMissingValue'][:]
assert_mask_matches(vardata, [False, False, False])
assert_equal(vardata, [1, 2, 3])
| 19,245 | 34.313761 | 137 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/tests/test_fortran.py
|
''' Tests for fortran sequential files '''
import tempfile
import shutil
from os import path, unlink
from glob import iglob
import re
from numpy.testing import assert_equal, assert_allclose
import numpy as np
from scipy.io import FortranFile, _test_fortran
DATA_PATH = path.join(path.dirname(__file__), 'data')
def test_fortranfiles_read():
for filename in iglob(path.join(DATA_PATH, "fortran-*-*x*x*.dat")):
m = re.search(r'fortran-([^-]+)-(\d+)x(\d+)x(\d+).dat', filename, re.I)
if not m:
raise RuntimeError("Couldn't match %s filename to regex" % filename)
dims = (int(m.group(2)), int(m.group(3)), int(m.group(4)))
dtype = m.group(1).replace('s', '<')
f = FortranFile(filename, 'r', '<u4')
data = f.read_record(dtype=dtype).reshape(dims, order='F')
f.close()
expected = np.arange(np.prod(dims)).reshape(dims).astype(dtype)
assert_equal(data, expected)
def test_fortranfiles_mixed_record():
filename = path.join(DATA_PATH, "fortran-mixed.dat")
with FortranFile(filename, 'r', '<u4') as f:
record = f.read_record('<i4,<f4,<i8,(2)<f8')
assert_equal(record['f0'][0], 1)
assert_allclose(record['f1'][0], 2.3)
assert_equal(record['f2'][0], 4)
assert_allclose(record['f3'][0], [5.6, 7.8])
def test_fortranfiles_write():
for filename in iglob(path.join(DATA_PATH, "fortran-*-*x*x*.dat")):
m = re.search(r'fortran-([^-]+)-(\d+)x(\d+)x(\d+).dat', filename, re.I)
if not m:
raise RuntimeError("Couldn't match %s filename to regex" % filename)
dims = (int(m.group(2)), int(m.group(3)), int(m.group(4)))
dtype = m.group(1).replace('s', '<')
data = np.arange(np.prod(dims)).reshape(dims).astype(dtype)
tmpdir = tempfile.mkdtemp()
try:
testFile = path.join(tmpdir,path.basename(filename))
f = FortranFile(testFile, 'w','<u4')
f.write_record(data.T)
f.close()
originalfile = open(filename, 'rb')
newfile = open(testFile, 'rb')
assert_equal(originalfile.read(), newfile.read(),
err_msg=filename)
originalfile.close()
newfile.close()
finally:
shutil.rmtree(tmpdir)
def test_fortranfile_read_mixed_record():
# The data file fortran-3x3d-2i.dat contains the program that
# produced it at the end.
#
# double precision :: a(3,3)
# integer :: b(2)
# ...
# open(1, file='fortran-3x3d-2i.dat', form='unformatted')
# write(1) a, b
# close(1)
#
filename = path.join(DATA_PATH, "fortran-3x3d-2i.dat")
with FortranFile(filename, 'r', '<u4') as f:
record = f.read_record('(3,3)f8', '2i4')
ax = np.arange(3*3).reshape(3, 3).astype(np.double)
bx = np.array([-1, -2], dtype=np.int32)
assert_equal(record[0], ax.T)
assert_equal(record[1], bx.T)
def test_fortranfile_write_mixed_record(tmpdir):
tf = path.join(str(tmpdir), 'test.dat')
records = [
(('f4', 'f4', 'i4'), (np.float32(2), np.float32(3), np.int32(100))),
(('4f4', '(3,3)f4', '8i4'), (np.random.randint(255, size=[4]).astype(np.float32),
np.random.randint(255, size=[3, 3]).astype(np.float32),
np.random.randint(255, size=[8]).astype(np.int32)))
]
for dtype, a in records:
with FortranFile(tf, 'w') as f:
f.write_record(*a)
with FortranFile(tf, 'r') as f:
b = f.read_record(*dtype)
assert_equal(len(a), len(b))
for aa, bb in zip(a, b):
assert_equal(bb, aa)
def test_fortran_roundtrip(tmpdir):
filename = path.join(str(tmpdir), 'test.dat')
np.random.seed(1)
# double precision
m, n, k = 5, 3, 2
a = np.random.randn(m, n, k)
with FortranFile(filename, 'w') as f:
f.write_record(a.T)
a2 = _test_fortran.read_unformatted_double(m, n, k, filename)
with FortranFile(filename, 'r') as f:
a3 = f.read_record('(2,3,5)f8').T
assert_equal(a2, a)
assert_equal(a3, a)
# integer
m, n, k = 5, 3, 2
a = np.random.randn(m, n, k).astype(np.int32)
with FortranFile(filename, 'w') as f:
f.write_record(a.T)
a2 = _test_fortran.read_unformatted_int(m, n, k, filename)
with FortranFile(filename, 'r') as f:
a3 = f.read_record('(2,3,5)i4').T
assert_equal(a2, a)
assert_equal(a3, a)
# mixed
m, n, k = 5, 3, 2
a = np.random.randn(m, n)
b = np.random.randn(k).astype(np.intc)
with FortranFile(filename, 'w') as f:
f.write_record(a.T, b.T)
a2, b2 = _test_fortran.read_unformatted_mixed(m, n, k, filename)
with FortranFile(filename, 'r') as f:
a3, b3 = f.read_record('(3,5)f8', '2i4')
a3 = a3.T
assert_equal(a2, a)
assert_equal(a3, a)
assert_equal(b2, b)
assert_equal(b3, b)
| 4,975 | 30.1 | 92 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/tests/test_wavfile.py
|
from __future__ import division, print_function, absolute_import
import os
import sys
import tempfile
from io import BytesIO
import numpy as np
from numpy.testing import assert_equal, assert_, assert_array_equal
from pytest import raises as assert_raises
from scipy._lib._numpy_compat import suppress_warnings
from scipy.io import wavfile
def datafile(fn):
return os.path.join(os.path.dirname(__file__), 'data', fn)
def test_read_1():
for mmap in [False, True]:
rate, data = wavfile.read(datafile('test-44100Hz-le-1ch-4bytes.wav'),
mmap=mmap)
assert_equal(rate, 44100)
assert_(np.issubdtype(data.dtype, np.int32))
assert_equal(data.shape, (4410,))
del data
def test_read_2():
for mmap in [False, True]:
rate, data = wavfile.read(datafile('test-8000Hz-le-2ch-1byteu.wav'),
mmap=mmap)
assert_equal(rate, 8000)
assert_(np.issubdtype(data.dtype, np.uint8))
assert_equal(data.shape, (800, 2))
del data
def test_read_3():
for mmap in [False, True]:
rate, data = wavfile.read(datafile('test-44100Hz-2ch-32bit-float-le.wav'),
mmap=mmap)
assert_equal(rate, 44100)
assert_(np.issubdtype(data.dtype, np.float32))
assert_equal(data.shape, (441, 2))
del data
def test_read_4():
for mmap in [False, True]:
with suppress_warnings() as sup:
sup.filter(wavfile.WavFileWarning,
"Chunk .non-data. not understood, skipping it")
rate, data = wavfile.read(datafile('test-48000Hz-2ch-64bit-float-le-wavex.wav'),
mmap=mmap)
assert_equal(rate, 48000)
assert_(np.issubdtype(data.dtype, np.float64))
assert_equal(data.shape, (480, 2))
del data
def test_read_5():
for mmap in [False, True]:
rate, data = wavfile.read(datafile('test-44100Hz-2ch-32bit-float-be.wav'),
mmap=mmap)
assert_equal(rate, 44100)
assert_(np.issubdtype(data.dtype, np.float32))
assert_(data.dtype.byteorder == '>' or (sys.byteorder == 'big' and
data.dtype.byteorder == '='))
assert_equal(data.shape, (441, 2))
del data
def test_read_fail():
for mmap in [False, True]:
fp = open(datafile('example_1.nc'), 'rb')
assert_raises(ValueError, wavfile.read, fp, mmap=mmap)
fp.close()
def test_read_early_eof():
for mmap in [False, True]:
fp = open(datafile('test-44100Hz-le-1ch-4bytes-early-eof.wav'), 'rb')
assert_raises(ValueError, wavfile.read, fp, mmap=mmap)
fp.close()
def test_read_incomplete_chunk():
for mmap in [False, True]:
fp = open(datafile('test-44100Hz-le-1ch-4bytes-incomplete-chunk.wav'), 'rb')
assert_raises(ValueError, wavfile.read, fp, mmap=mmap)
fp.close()
def _check_roundtrip(realfile, rate, dtype, channels):
if realfile:
fd, tmpfile = tempfile.mkstemp(suffix='.wav')
os.close(fd)
else:
tmpfile = BytesIO()
try:
data = np.random.rand(100, channels)
if channels == 1:
data = data[:,0]
if dtype.kind == 'f':
# The range of the float type should be in [-1, 1]
data = data.astype(dtype)
else:
data = (data*128).astype(dtype)
wavfile.write(tmpfile, rate, data)
for mmap in [False, True]:
rate2, data2 = wavfile.read(tmpfile, mmap=mmap)
assert_equal(rate, rate2)
assert_(data2.dtype.byteorder in ('<', '=', '|'), msg=data2.dtype)
assert_array_equal(data, data2)
del data2
finally:
if realfile:
os.unlink(tmpfile)
def test_write_roundtrip():
for realfile in (False, True):
for dtypechar in ('i', 'u', 'f', 'g', 'q'):
for size in (1, 2, 4, 8):
if size == 1 and dtypechar == 'i':
# signed 8-bit integer PCM is not allowed
continue
if size > 1 and dtypechar == 'u':
# unsigned > 8-bit integer PCM is not allowed
continue
if (size == 1 or size == 2) and dtypechar == 'f':
# 8- or 16-bit float PCM is not expected
continue
if dtypechar in 'gq':
# no size allowed for these types
if size == 1:
size = ''
else:
continue
for endianness in ('>', '<'):
if size == 1 and endianness == '<':
continue
for rate in (8000, 32000):
for channels in (1, 2, 5):
dt = np.dtype('%s%s%s' % (endianness, dtypechar, size))
_check_roundtrip(realfile, rate, dt, channels)
| 5,111 | 30.95 | 92 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/tests/test_idl.py
|
from __future__ import division, print_function, absolute_import
from os import path
import warnings
DATA_PATH = path.join(path.dirname(__file__), 'data')
import numpy as np
from numpy.testing import (assert_equal, assert_array_equal,
assert_)
from scipy._lib._numpy_compat import suppress_warnings
from scipy.io.idl import readsav
def object_array(*args):
"""Constructs a numpy array of objects"""
array = np.empty(len(args), dtype=object)
for i in range(len(args)):
array[i] = args[i]
return array
def assert_identical(a, b):
"""Assert whether value AND type are the same"""
assert_equal(a, b)
if type(b) is str:
assert_equal(type(a), type(b))
else:
assert_equal(np.asarray(a).dtype.type, np.asarray(b).dtype.type)
def assert_array_identical(a, b):
"""Assert whether values AND type are the same"""
assert_array_equal(a, b)
assert_equal(a.dtype.type, b.dtype.type)
# Define vectorized ID function for pointer arrays
vect_id = np.vectorize(id)
class TestIdict:
def test_idict(self):
custom_dict = {'a': np.int16(999)}
original_id = id(custom_dict)
s = readsav(path.join(DATA_PATH, 'scalar_byte.sav'), idict=custom_dict, verbose=False)
assert_equal(original_id, id(s))
assert_('a' in s)
assert_identical(s['a'], np.int16(999))
assert_identical(s['i8u'], np.uint8(234))
class TestScalars:
# Test that scalar values are read in with the correct value and type
def test_byte(self):
s = readsav(path.join(DATA_PATH, 'scalar_byte.sav'), verbose=False)
assert_identical(s.i8u, np.uint8(234))
def test_int16(self):
s = readsav(path.join(DATA_PATH, 'scalar_int16.sav'), verbose=False)
assert_identical(s.i16s, np.int16(-23456))
def test_int32(self):
s = readsav(path.join(DATA_PATH, 'scalar_int32.sav'), verbose=False)
assert_identical(s.i32s, np.int32(-1234567890))
def test_float32(self):
s = readsav(path.join(DATA_PATH, 'scalar_float32.sav'), verbose=False)
assert_identical(s.f32, np.float32(-3.1234567e+37))
def test_float64(self):
s = readsav(path.join(DATA_PATH, 'scalar_float64.sav'), verbose=False)
assert_identical(s.f64, np.float64(-1.1976931348623157e+307))
def test_complex32(self):
s = readsav(path.join(DATA_PATH, 'scalar_complex32.sav'), verbose=False)
assert_identical(s.c32, np.complex64(3.124442e13-2.312442e31j))
def test_bytes(self):
s = readsav(path.join(DATA_PATH, 'scalar_string.sav'), verbose=False)
assert_identical(s.s, np.bytes_("The quick brown fox jumps over the lazy python"))
def test_structure(self):
pass
def test_complex64(self):
s = readsav(path.join(DATA_PATH, 'scalar_complex64.sav'), verbose=False)
assert_identical(s.c64, np.complex128(1.1987253647623157e+112-5.1987258887729157e+307j))
def test_heap_pointer(self):
pass
def test_object_reference(self):
pass
def test_uint16(self):
s = readsav(path.join(DATA_PATH, 'scalar_uint16.sav'), verbose=False)
assert_identical(s.i16u, np.uint16(65511))
def test_uint32(self):
s = readsav(path.join(DATA_PATH, 'scalar_uint32.sav'), verbose=False)
assert_identical(s.i32u, np.uint32(4294967233))
def test_int64(self):
s = readsav(path.join(DATA_PATH, 'scalar_int64.sav'), verbose=False)
assert_identical(s.i64s, np.int64(-9223372036854774567))
def test_uint64(self):
s = readsav(path.join(DATA_PATH, 'scalar_uint64.sav'), verbose=False)
assert_identical(s.i64u, np.uint64(18446744073709529285))
class TestCompressed(TestScalars):
# Test that compressed .sav files can be read in
def test_compressed(self):
s = readsav(path.join(DATA_PATH, 'various_compressed.sav'), verbose=False)
assert_identical(s.i8u, np.uint8(234))
assert_identical(s.f32, np.float32(-3.1234567e+37))
assert_identical(s.c64, np.complex128(1.1987253647623157e+112-5.1987258887729157e+307j))
assert_equal(s.array5d.shape, (4, 3, 4, 6, 5))
assert_identical(s.arrays.a[0], np.array([1, 2, 3], dtype=np.int16))
assert_identical(s.arrays.b[0], np.array([4., 5., 6., 7.], dtype=np.float32))
assert_identical(s.arrays.c[0], np.array([np.complex64(1+2j), np.complex64(7+8j)]))
assert_identical(s.arrays.d[0], np.array([b"cheese", b"bacon", b"spam"], dtype=object))
class TestArrayDimensions:
# Test that multi-dimensional arrays are read in with the correct dimensions
def test_1d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_1d.sav'), verbose=False)
assert_equal(s.array1d.shape, (123, ))
def test_2d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_2d.sav'), verbose=False)
assert_equal(s.array2d.shape, (22, 12))
def test_3d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_3d.sav'), verbose=False)
assert_equal(s.array3d.shape, (11, 22, 12))
def test_4d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_4d.sav'), verbose=False)
assert_equal(s.array4d.shape, (4, 5, 8, 7))
def test_5d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_5d.sav'), verbose=False)
assert_equal(s.array5d.shape, (4, 3, 4, 6, 5))
def test_6d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_6d.sav'), verbose=False)
assert_equal(s.array6d.shape, (3, 6, 4, 5, 3, 4))
def test_7d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_7d.sav'), verbose=False)
assert_equal(s.array7d.shape, (2, 1, 2, 3, 4, 3, 2))
def test_8d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_8d.sav'), verbose=False)
assert_equal(s.array8d.shape, (4, 3, 2, 1, 2, 3, 5, 4))
class TestStructures:
def test_scalars(self):
s = readsav(path.join(DATA_PATH, 'struct_scalars.sav'), verbose=False)
assert_identical(s.scalars.a, np.array(np.int16(1)))
assert_identical(s.scalars.b, np.array(np.int32(2)))
assert_identical(s.scalars.c, np.array(np.float32(3.)))
assert_identical(s.scalars.d, np.array(np.float64(4.)))
assert_identical(s.scalars.e, np.array([b"spam"], dtype=object))
assert_identical(s.scalars.f, np.array(np.complex64(-1.+3j)))
def test_scalars_replicated(self):
s = readsav(path.join(DATA_PATH, 'struct_scalars_replicated.sav'), verbose=False)
assert_identical(s.scalars_rep.a, np.repeat(np.int16(1), 5))
assert_identical(s.scalars_rep.b, np.repeat(np.int32(2), 5))
assert_identical(s.scalars_rep.c, np.repeat(np.float32(3.), 5))
assert_identical(s.scalars_rep.d, np.repeat(np.float64(4.), 5))
assert_identical(s.scalars_rep.e, np.repeat(b"spam", 5).astype(object))
assert_identical(s.scalars_rep.f, np.repeat(np.complex64(-1.+3j), 5))
def test_scalars_replicated_3d(self):
s = readsav(path.join(DATA_PATH, 'struct_scalars_replicated_3d.sav'), verbose=False)
assert_identical(s.scalars_rep.a, np.repeat(np.int16(1), 24).reshape(4, 3, 2))
assert_identical(s.scalars_rep.b, np.repeat(np.int32(2), 24).reshape(4, 3, 2))
assert_identical(s.scalars_rep.c, np.repeat(np.float32(3.), 24).reshape(4, 3, 2))
assert_identical(s.scalars_rep.d, np.repeat(np.float64(4.), 24).reshape(4, 3, 2))
assert_identical(s.scalars_rep.e, np.repeat(b"spam", 24).reshape(4, 3, 2).astype(object))
assert_identical(s.scalars_rep.f, np.repeat(np.complex64(-1.+3j), 24).reshape(4, 3, 2))
def test_arrays(self):
s = readsav(path.join(DATA_PATH, 'struct_arrays.sav'), verbose=False)
assert_array_identical(s.arrays.a[0], np.array([1, 2, 3], dtype=np.int16))
assert_array_identical(s.arrays.b[0], np.array([4., 5., 6., 7.], dtype=np.float32))
assert_array_identical(s.arrays.c[0], np.array([np.complex64(1+2j), np.complex64(7+8j)]))
assert_array_identical(s.arrays.d[0], np.array([b"cheese", b"bacon", b"spam"], dtype=object))
def test_arrays_replicated(self):
s = readsav(path.join(DATA_PATH, 'struct_arrays_replicated.sav'), verbose=False)
# Check column types
assert_(s.arrays_rep.a.dtype.type is np.object_)
assert_(s.arrays_rep.b.dtype.type is np.object_)
assert_(s.arrays_rep.c.dtype.type is np.object_)
assert_(s.arrays_rep.d.dtype.type is np.object_)
# Check column shapes
assert_equal(s.arrays_rep.a.shape, (5, ))
assert_equal(s.arrays_rep.b.shape, (5, ))
assert_equal(s.arrays_rep.c.shape, (5, ))
assert_equal(s.arrays_rep.d.shape, (5, ))
# Check values
for i in range(5):
assert_array_identical(s.arrays_rep.a[i],
np.array([1, 2, 3], dtype=np.int16))
assert_array_identical(s.arrays_rep.b[i],
np.array([4., 5., 6., 7.], dtype=np.float32))
assert_array_identical(s.arrays_rep.c[i],
np.array([np.complex64(1+2j),
np.complex64(7+8j)]))
assert_array_identical(s.arrays_rep.d[i],
np.array([b"cheese", b"bacon", b"spam"],
dtype=object))
def test_arrays_replicated_3d(self):
s = readsav(path.join(DATA_PATH, 'struct_arrays_replicated_3d.sav'), verbose=False)
# Check column types
assert_(s.arrays_rep.a.dtype.type is np.object_)
assert_(s.arrays_rep.b.dtype.type is np.object_)
assert_(s.arrays_rep.c.dtype.type is np.object_)
assert_(s.arrays_rep.d.dtype.type is np.object_)
# Check column shapes
assert_equal(s.arrays_rep.a.shape, (4, 3, 2))
assert_equal(s.arrays_rep.b.shape, (4, 3, 2))
assert_equal(s.arrays_rep.c.shape, (4, 3, 2))
assert_equal(s.arrays_rep.d.shape, (4, 3, 2))
# Check values
for i in range(4):
for j in range(3):
for k in range(2):
assert_array_identical(s.arrays_rep.a[i, j, k],
np.array([1, 2, 3], dtype=np.int16))
assert_array_identical(s.arrays_rep.b[i, j, k],
np.array([4., 5., 6., 7.],
dtype=np.float32))
assert_array_identical(s.arrays_rep.c[i, j, k],
np.array([np.complex64(1+2j),
np.complex64(7+8j)]))
assert_array_identical(s.arrays_rep.d[i, j, k],
np.array([b"cheese", b"bacon", b"spam"],
dtype=object))
def test_inheritance(self):
s = readsav(path.join(DATA_PATH, 'struct_inherit.sav'), verbose=False)
assert_identical(s.fc.x, np.array([0], dtype=np.int16))
assert_identical(s.fc.y, np.array([0], dtype=np.int16))
assert_identical(s.fc.r, np.array([0], dtype=np.int16))
assert_identical(s.fc.c, np.array([4], dtype=np.int16))
def test_arrays_corrupt_idl80(self):
# test byte arrays with missing nbyte information from IDL 8.0 .sav file
with suppress_warnings() as sup:
sup.filter(UserWarning, "Not able to verify number of bytes from header")
s = readsav(path.join(DATA_PATH,'struct_arrays_byte_idl80.sav'),
verbose=False)
assert_identical(s.y.x[0], np.array([55,66], dtype=np.uint8))
class TestPointers:
# Check that pointers in .sav files produce references to the same object in Python
def test_pointers(self):
s = readsav(path.join(DATA_PATH, 'scalar_heap_pointer.sav'), verbose=False)
assert_identical(s.c64_pointer1, np.complex128(1.1987253647623157e+112-5.1987258887729157e+307j))
assert_identical(s.c64_pointer2, np.complex128(1.1987253647623157e+112-5.1987258887729157e+307j))
assert_(s.c64_pointer1 is s.c64_pointer2)
class TestPointerArray:
# Test that pointers in arrays are correctly read in
def test_1d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_pointer_1d.sav'), verbose=False)
assert_equal(s.array1d.shape, (123, ))
assert_(np.all(s.array1d == np.float32(4.)))
assert_(np.all(vect_id(s.array1d) == id(s.array1d[0])))
def test_2d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_pointer_2d.sav'), verbose=False)
assert_equal(s.array2d.shape, (22, 12))
assert_(np.all(s.array2d == np.float32(4.)))
assert_(np.all(vect_id(s.array2d) == id(s.array2d[0,0])))
def test_3d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_pointer_3d.sav'), verbose=False)
assert_equal(s.array3d.shape, (11, 22, 12))
assert_(np.all(s.array3d == np.float32(4.)))
assert_(np.all(vect_id(s.array3d) == id(s.array3d[0,0,0])))
def test_4d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_pointer_4d.sav'), verbose=False)
assert_equal(s.array4d.shape, (4, 5, 8, 7))
assert_(np.all(s.array4d == np.float32(4.)))
assert_(np.all(vect_id(s.array4d) == id(s.array4d[0,0,0,0])))
def test_5d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_pointer_5d.sav'), verbose=False)
assert_equal(s.array5d.shape, (4, 3, 4, 6, 5))
assert_(np.all(s.array5d == np.float32(4.)))
assert_(np.all(vect_id(s.array5d) == id(s.array5d[0,0,0,0,0])))
def test_6d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_pointer_6d.sav'), verbose=False)
assert_equal(s.array6d.shape, (3, 6, 4, 5, 3, 4))
assert_(np.all(s.array6d == np.float32(4.)))
assert_(np.all(vect_id(s.array6d) == id(s.array6d[0,0,0,0,0,0])))
def test_7d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_pointer_7d.sav'), verbose=False)
assert_equal(s.array7d.shape, (2, 1, 2, 3, 4, 3, 2))
assert_(np.all(s.array7d == np.float32(4.)))
assert_(np.all(vect_id(s.array7d) == id(s.array7d[0,0,0,0,0,0,0])))
def test_8d(self):
s = readsav(path.join(DATA_PATH, 'array_float32_pointer_8d.sav'), verbose=False)
assert_equal(s.array8d.shape, (4, 3, 2, 1, 2, 3, 5, 4))
assert_(np.all(s.array8d == np.float32(4.)))
assert_(np.all(vect_id(s.array8d) == id(s.array8d[0,0,0,0,0,0,0,0])))
class TestPointerStructures:
# Test that structures are correctly read in
def test_scalars(self):
s = readsav(path.join(DATA_PATH, 'struct_pointers.sav'), verbose=False)
assert_identical(s.pointers.g, np.array(np.float32(4.), dtype=np.object_))
assert_identical(s.pointers.h, np.array(np.float32(4.), dtype=np.object_))
assert_(id(s.pointers.g[0]) == id(s.pointers.h[0]))
def test_pointers_replicated(self):
s = readsav(path.join(DATA_PATH, 'struct_pointers_replicated.sav'), verbose=False)
assert_identical(s.pointers_rep.g, np.repeat(np.float32(4.), 5).astype(np.object_))
assert_identical(s.pointers_rep.h, np.repeat(np.float32(4.), 5).astype(np.object_))
assert_(np.all(vect_id(s.pointers_rep.g) == vect_id(s.pointers_rep.h)))
def test_pointers_replicated_3d(self):
s = readsav(path.join(DATA_PATH, 'struct_pointers_replicated_3d.sav'), verbose=False)
s_expect = np.repeat(np.float32(4.), 24).reshape(4, 3, 2).astype(np.object_)
assert_identical(s.pointers_rep.g, s_expect)
assert_identical(s.pointers_rep.h, s_expect)
assert_(np.all(vect_id(s.pointers_rep.g) == vect_id(s.pointers_rep.h)))
def test_arrays(self):
s = readsav(path.join(DATA_PATH, 'struct_pointer_arrays.sav'), verbose=False)
assert_array_identical(s.arrays.g[0], np.repeat(np.float32(4.), 2).astype(np.object_))
assert_array_identical(s.arrays.h[0], np.repeat(np.float32(4.), 3).astype(np.object_))
assert_(np.all(vect_id(s.arrays.g[0]) == id(s.arrays.g[0][0])))
assert_(np.all(vect_id(s.arrays.h[0]) == id(s.arrays.h[0][0])))
assert_(id(s.arrays.g[0][0]) == id(s.arrays.h[0][0]))
def test_arrays_replicated(self):
s = readsav(path.join(DATA_PATH, 'struct_pointer_arrays_replicated.sav'), verbose=False)
# Check column types
assert_(s.arrays_rep.g.dtype.type is np.object_)
assert_(s.arrays_rep.h.dtype.type is np.object_)
# Check column shapes
assert_equal(s.arrays_rep.g.shape, (5, ))
assert_equal(s.arrays_rep.h.shape, (5, ))
# Check values
for i in range(5):
assert_array_identical(s.arrays_rep.g[i], np.repeat(np.float32(4.), 2).astype(np.object_))
assert_array_identical(s.arrays_rep.h[i], np.repeat(np.float32(4.), 3).astype(np.object_))
assert_(np.all(vect_id(s.arrays_rep.g[i]) == id(s.arrays_rep.g[0][0])))
assert_(np.all(vect_id(s.arrays_rep.h[i]) == id(s.arrays_rep.h[0][0])))
def test_arrays_replicated_3d(self):
pth = path.join(DATA_PATH, 'struct_pointer_arrays_replicated_3d.sav')
s = readsav(pth, verbose=False)
# Check column types
assert_(s.arrays_rep.g.dtype.type is np.object_)
assert_(s.arrays_rep.h.dtype.type is np.object_)
# Check column shapes
assert_equal(s.arrays_rep.g.shape, (4, 3, 2))
assert_equal(s.arrays_rep.h.shape, (4, 3, 2))
# Check values
for i in range(4):
for j in range(3):
for k in range(2):
assert_array_identical(s.arrays_rep.g[i, j, k],
np.repeat(np.float32(4.), 2).astype(np.object_))
assert_array_identical(s.arrays_rep.h[i, j, k],
np.repeat(np.float32(4.), 3).astype(np.object_))
assert_(np.all(vect_id(s.arrays_rep.g[i, j, k]) == id(s.arrays_rep.g[0, 0, 0][0])))
assert_(np.all(vect_id(s.arrays_rep.h[i, j, k]) == id(s.arrays_rep.h[0, 0, 0][0])))
class TestTags:
'''Test that sav files with description tag read at all'''
def test_description(self):
s = readsav(path.join(DATA_PATH, 'scalar_byte_descr.sav'), verbose=False)
assert_identical(s.i8u, np.uint8(234))
def test_null_pointer():
# Regression test for null pointers.
s = readsav(path.join(DATA_PATH, 'null_pointer.sav'), verbose=False)
assert_identical(s.point, None)
assert_identical(s.check, np.int16(5))
def test_invalid_pointer():
# Regression test for invalid pointers (gh-4613).
# In some files in the wild, pointers can sometimes refer to a heap
# variable that does not exist. In that case, we now gracefully fail for
# that variable and replace the variable with None and emit a warning.
# Since it's difficult to artificially produce such files, the file used
# here has been edited to force the pointer reference to be invalid.
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
s = readsav(path.join(DATA_PATH, 'invalid_pointer.sav'), verbose=False)
assert_(len(w) == 1)
assert_(str(w[0].message) == ("Variable referenced by pointer not found in "
"heap: variable will be set to None"))
assert_identical(s['a'], np.array([None, None]))
| 19,683 | 43.433409 | 105 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/io/tests/test_mmio.py
|
from __future__ import division, print_function, absolute_import
from tempfile import mkdtemp, mktemp
import os
import shutil
import numpy as np
from numpy import array, transpose, pi
from numpy.testing import (assert_equal,
assert_array_equal, assert_array_almost_equal)
import pytest
from pytest import raises as assert_raises
import scipy.sparse
from scipy.io.mmio import mminfo, mmread, mmwrite
parametrize_args = [('integer', 'int'),
('unsigned-integer', 'uint')]
class TestMMIOArray(object):
def setup_method(self):
self.tmpdir = mkdtemp()
self.fn = os.path.join(self.tmpdir, 'testfile.mtx')
def teardown_method(self):
shutil.rmtree(self.tmpdir)
def check(self, a, info):
mmwrite(self.fn, a)
assert_equal(mminfo(self.fn), info)
b = mmread(self.fn)
assert_array_almost_equal(a, b)
def check_exact(self, a, info):
mmwrite(self.fn, a)
assert_equal(mminfo(self.fn), info)
b = mmread(self.fn)
assert_equal(a, b)
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_integer(self, typeval, dtype):
self.check_exact(array([[1, 2], [3, 4]], dtype=dtype),
(2, 2, 4, 'array', typeval, 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_32bit_integer(self, typeval, dtype):
a = array([[2**31-1, 2**31-2], [2**31-3, 2**31-4]], dtype=dtype)
self.check_exact(a, (2, 2, 4, 'array', typeval, 'general'))
def test_64bit_integer(self):
a = array([[2**31, 2**32], [2**63-2, 2**63-1]], dtype=np.int64)
if (np.intp(0).itemsize < 8):
assert_raises(OverflowError, mmwrite, self.fn, a)
else:
self.check_exact(a, (2, 2, 4, 'array', 'integer', 'general'))
def test_64bit_unsigned_integer(self):
a = array([[2**31, 2**32], [2**64-2, 2**64-1]], dtype=np.uint64)
self.check_exact(a, (2, 2, 4, 'array', 'unsigned-integer', 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_upper_triangle_integer(self, typeval, dtype):
self.check_exact(array([[0, 1], [0, 0]], dtype=dtype),
(2, 2, 4, 'array', typeval, 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_lower_triangle_integer(self, typeval, dtype):
self.check_exact(array([[0, 0], [1, 0]], dtype=dtype),
(2, 2, 4, 'array', typeval, 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_rectangular_integer(self, typeval, dtype):
self.check_exact(array([[1, 2, 3], [4, 5, 6]], dtype=dtype),
(2, 3, 6, 'array', typeval, 'general'))
def test_simple_rectangular_float(self):
self.check([[1, 2], [3.5, 4], [5, 6]],
(3, 2, 6, 'array', 'real', 'general'))
def test_simple_float(self):
self.check([[1, 2], [3, 4.0]],
(2, 2, 4, 'array', 'real', 'general'))
def test_simple_complex(self):
self.check([[1, 2], [3, 4j]],
(2, 2, 4, 'array', 'complex', 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_symmetric_integer(self, typeval, dtype):
self.check_exact(array([[1, 2], [2, 4]], dtype=dtype),
(2, 2, 4, 'array', typeval, 'symmetric'))
def test_simple_skew_symmetric_integer(self):
self.check_exact([[0, 2], [-2, 0]],
(2, 2, 4, 'array', 'integer', 'skew-symmetric'))
def test_simple_skew_symmetric_float(self):
self.check(array([[0, 2], [-2.0, 0.0]], 'f'),
(2, 2, 4, 'array', 'real', 'skew-symmetric'))
def test_simple_hermitian_complex(self):
self.check([[1, 2+3j], [2-3j, 4]],
(2, 2, 4, 'array', 'complex', 'hermitian'))
def test_random_symmetric_float(self):
sz = (20, 20)
a = np.random.random(sz)
a = a + transpose(a)
self.check(a, (20, 20, 400, 'array', 'real', 'symmetric'))
def test_random_rectangular_float(self):
sz = (20, 15)
a = np.random.random(sz)
self.check(a, (20, 15, 300, 'array', 'real', 'general'))
class TestMMIOSparseCSR(TestMMIOArray):
def setup_method(self):
self.tmpdir = mkdtemp()
self.fn = os.path.join(self.tmpdir, 'testfile.mtx')
def teardown_method(self):
shutil.rmtree(self.tmpdir)
def check(self, a, info):
mmwrite(self.fn, a)
assert_equal(mminfo(self.fn), info)
b = mmread(self.fn)
assert_array_almost_equal(a.todense(), b.todense())
def check_exact(self, a, info):
mmwrite(self.fn, a)
assert_equal(mminfo(self.fn), info)
b = mmread(self.fn)
assert_equal(a.todense(), b.todense())
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_integer(self, typeval, dtype):
self.check_exact(scipy.sparse.csr_matrix([[1, 2], [3, 4]], dtype=dtype),
(2, 2, 4, 'coordinate', typeval, 'general'))
def test_32bit_integer(self):
a = scipy.sparse.csr_matrix(array([[2**31-1, -2**31+2],
[2**31-3, 2**31-4]],
dtype=np.int32))
self.check_exact(a, (2, 2, 4, 'coordinate', 'integer', 'general'))
def test_64bit_integer(self):
a = scipy.sparse.csr_matrix(array([[2**32+1, 2**32+1],
[-2**63+2, 2**63-2]],
dtype=np.int64))
if (np.intp(0).itemsize < 8):
assert_raises(OverflowError, mmwrite, self.fn, a)
else:
self.check_exact(a, (2, 2, 4, 'coordinate', 'integer', 'general'))
def test_32bit_unsigned_integer(self):
a = scipy.sparse.csr_matrix(array([[2**31-1, 2**31-2],
[2**31-3, 2**31-4]],
dtype=np.uint32))
self.check_exact(a, (2, 2, 4, 'coordinate', 'unsigned-integer', 'general'))
def test_64bit_unsigned_integer(self):
a = scipy.sparse.csr_matrix(array([[2**32+1, 2**32+1],
[2**64-2, 2**64-1]],
dtype=np.uint64))
self.check_exact(a, (2, 2, 4, 'coordinate', 'unsigned-integer', 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_upper_triangle_integer(self, typeval, dtype):
self.check_exact(scipy.sparse.csr_matrix([[0, 1], [0, 0]], dtype=dtype),
(2, 2, 1, 'coordinate', typeval, 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_lower_triangle_integer(self, typeval, dtype):
self.check_exact(scipy.sparse.csr_matrix([[0, 0], [1, 0]], dtype=dtype),
(2, 2, 1, 'coordinate', typeval, 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_rectangular_integer(self, typeval, dtype):
self.check_exact(scipy.sparse.csr_matrix([[1, 2, 3], [4, 5, 6]], dtype=dtype),
(2, 3, 6, 'coordinate', typeval, 'general'))
def test_simple_rectangular_float(self):
self.check(scipy.sparse.csr_matrix([[1, 2], [3.5, 4], [5, 6]]),
(3, 2, 6, 'coordinate', 'real', 'general'))
def test_simple_float(self):
self.check(scipy.sparse.csr_matrix([[1, 2], [3, 4.0]]),
(2, 2, 4, 'coordinate', 'real', 'general'))
def test_simple_complex(self):
self.check(scipy.sparse.csr_matrix([[1, 2], [3, 4j]]),
(2, 2, 4, 'coordinate', 'complex', 'general'))
@pytest.mark.parametrize('typeval, dtype', parametrize_args)
def test_simple_symmetric_integer(self, typeval, dtype):
self.check_exact(scipy.sparse.csr_matrix([[1, 2], [2, 4]], dtype=dtype),
(2, 2, 3, 'coordinate', typeval, 'symmetric'))
def test_simple_skew_symmetric_integer(self):
self.check_exact(scipy.sparse.csr_matrix([[1, 2], [-2, 4]]),
(2, 2, 3, 'coordinate', 'integer', 'skew-symmetric'))
def test_simple_skew_symmetric_float(self):
self.check(scipy.sparse.csr_matrix(array([[1, 2], [-2.0, 4]], 'f')),
(2, 2, 3, 'coordinate', 'real', 'skew-symmetric'))
def test_simple_hermitian_complex(self):
self.check(scipy.sparse.csr_matrix([[1, 2+3j], [2-3j, 4]]),
(2, 2, 3, 'coordinate', 'complex', 'hermitian'))
def test_random_symmetric_float(self):
sz = (20, 20)
a = np.random.random(sz)
a = a + transpose(a)
a = scipy.sparse.csr_matrix(a)
self.check(a, (20, 20, 210, 'coordinate', 'real', 'symmetric'))
def test_random_rectangular_float(self):
sz = (20, 15)
a = np.random.random(sz)
a = scipy.sparse.csr_matrix(a)
self.check(a, (20, 15, 300, 'coordinate', 'real', 'general'))
def test_simple_pattern(self):
a = scipy.sparse.csr_matrix([[0, 1.5], [3.0, 2.5]])
p = np.zeros_like(a.todense())
p[a.todense() > 0] = 1
info = (2, 2, 3, 'coordinate', 'pattern', 'general')
mmwrite(self.fn, a, field='pattern')
assert_equal(mminfo(self.fn), info)
b = mmread(self.fn)
assert_array_almost_equal(p, b.todense())
_32bit_integer_dense_example = '''\
%%MatrixMarket matrix array integer general
2 2
2147483647
2147483646
2147483647
2147483646
'''
_32bit_integer_sparse_example = '''\
%%MatrixMarket matrix coordinate integer symmetric
2 2 2
1 1 2147483647
2 2 2147483646
'''
_64bit_integer_dense_example = '''\
%%MatrixMarket matrix array integer general
2 2
2147483648
-9223372036854775806
-2147483648
9223372036854775807
'''
_64bit_integer_sparse_general_example = '''\
%%MatrixMarket matrix coordinate integer general
2 2 3
1 1 2147483648
1 2 9223372036854775807
2 2 9223372036854775807
'''
_64bit_integer_sparse_symmetric_example = '''\
%%MatrixMarket matrix coordinate integer symmetric
2 2 3
1 1 2147483648
1 2 -9223372036854775807
2 2 9223372036854775807
'''
_64bit_integer_sparse_skew_example = '''\
%%MatrixMarket matrix coordinate integer skew-symmetric
2 2 3
1 1 2147483648
1 2 -9223372036854775807
2 2 9223372036854775807
'''
_over64bit_integer_dense_example = '''\
%%MatrixMarket matrix array integer general
2 2
2147483648
9223372036854775807
2147483648
9223372036854775808
'''
_over64bit_integer_sparse_example = '''\
%%MatrixMarket matrix coordinate integer symmetric
2 2 2
1 1 2147483648
2 2 19223372036854775808
'''
class TestMMIOReadLargeIntegers(object):
def setup_method(self):
self.tmpdir = mkdtemp()
self.fn = os.path.join(self.tmpdir, 'testfile.mtx')
def teardown_method(self):
shutil.rmtree(self.tmpdir)
def check_read(self, example, a, info, dense, over32, over64):
with open(self.fn, 'w') as f:
f.write(example)
assert_equal(mminfo(self.fn), info)
if (over32 and (np.intp(0).itemsize < 8)) or over64:
assert_raises(OverflowError, mmread, self.fn)
else:
b = mmread(self.fn)
if not dense:
b = b.todense()
assert_equal(a, b)
def test_read_32bit_integer_dense(self):
a = array([[2**31-1, 2**31-1],
[2**31-2, 2**31-2]], dtype=np.int64)
self.check_read(_32bit_integer_dense_example,
a,
(2, 2, 4, 'array', 'integer', 'general'),
dense=True,
over32=False,
over64=False)
def test_read_32bit_integer_sparse(self):
a = array([[2**31-1, 0],
[0, 2**31-2]], dtype=np.int64)
self.check_read(_32bit_integer_sparse_example,
a,
(2, 2, 2, 'coordinate', 'integer', 'symmetric'),
dense=False,
over32=False,
over64=False)
def test_read_64bit_integer_dense(self):
a = array([[2**31, -2**31],
[-2**63+2, 2**63-1]], dtype=np.int64)
self.check_read(_64bit_integer_dense_example,
a,
(2, 2, 4, 'array', 'integer', 'general'),
dense=True,
over32=True,
over64=False)
def test_read_64bit_integer_sparse_general(self):
a = array([[2**31, 2**63-1],
[0, 2**63-1]], dtype=np.int64)
self.check_read(_64bit_integer_sparse_general_example,
a,
(2, 2, 3, 'coordinate', 'integer', 'general'),
dense=False,
over32=True,
over64=False)
def test_read_64bit_integer_sparse_symmetric(self):
a = array([[2**31, -2**63+1],
[-2**63+1, 2**63-1]], dtype=np.int64)
self.check_read(_64bit_integer_sparse_symmetric_example,
a,
(2, 2, 3, 'coordinate', 'integer', 'symmetric'),
dense=False,
over32=True,
over64=False)
def test_read_64bit_integer_sparse_skew(self):
a = array([[2**31, -2**63+1],
[2**63-1, 2**63-1]], dtype=np.int64)
self.check_read(_64bit_integer_sparse_skew_example,
a,
(2, 2, 3, 'coordinate', 'integer', 'skew-symmetric'),
dense=False,
over32=True,
over64=False)
def test_read_over64bit_integer_dense(self):
self.check_read(_over64bit_integer_dense_example,
None,
(2, 2, 4, 'array', 'integer', 'general'),
dense=True,
over32=True,
over64=True)
def test_read_over64bit_integer_sparse(self):
self.check_read(_over64bit_integer_sparse_example,
None,
(2, 2, 2, 'coordinate', 'integer', 'symmetric'),
dense=False,
over32=True,
over64=True)
_general_example = '''\
%%MatrixMarket matrix coordinate real general
%=================================================================================
%
% This ASCII file represents a sparse MxN matrix with L
% nonzeros in the following Matrix Market format:
%
% +----------------------------------------------+
% |%%MatrixMarket matrix coordinate real general | <--- header line
% |% | <--+
% |% comments | |-- 0 or more comment lines
% |% | <--+
% | M N L | <--- rows, columns, entries
% | I1 J1 A(I1, J1) | <--+
% | I2 J2 A(I2, J2) | |
% | I3 J3 A(I3, J3) | |-- L lines
% | . . . | |
% | IL JL A(IL, JL) | <--+
% +----------------------------------------------+
%
% Indices are 1-based, i.e. A(1,1) is the first element.
%
%=================================================================================
5 5 8
1 1 1.000e+00
2 2 1.050e+01
3 3 1.500e-02
1 4 6.000e+00
4 2 2.505e+02
4 4 -2.800e+02
4 5 3.332e+01
5 5 1.200e+01
'''
_hermitian_example = '''\
%%MatrixMarket matrix coordinate complex hermitian
5 5 7
1 1 1.0 0
2 2 10.5 0
4 2 250.5 22.22
3 3 1.5e-2 0
4 4 -2.8e2 0
5 5 12. 0
5 4 0 33.32
'''
_skew_example = '''\
%%MatrixMarket matrix coordinate real skew-symmetric
5 5 7
1 1 1.0
2 2 10.5
4 2 250.5
3 3 1.5e-2
4 4 -2.8e2
5 5 12.
5 4 0
'''
_symmetric_example = '''\
%%MatrixMarket matrix coordinate real symmetric
5 5 7
1 1 1.0
2 2 10.5
4 2 250.5
3 3 1.5e-2
4 4 -2.8e2
5 5 12.
5 4 8
'''
_symmetric_pattern_example = '''\
%%MatrixMarket matrix coordinate pattern symmetric
5 5 7
1 1
2 2
4 2
3 3
4 4
5 5
5 4
'''
class TestMMIOCoordinate(object):
def setup_method(self):
self.tmpdir = mkdtemp()
self.fn = os.path.join(self.tmpdir, 'testfile.mtx')
def teardown_method(self):
shutil.rmtree(self.tmpdir)
def check_read(self, example, a, info):
f = open(self.fn, 'w')
f.write(example)
f.close()
assert_equal(mminfo(self.fn), info)
b = mmread(self.fn).todense()
assert_array_almost_equal(a, b)
def test_read_general(self):
a = [[1, 0, 0, 6, 0],
[0, 10.5, 0, 0, 0],
[0, 0, .015, 0, 0],
[0, 250.5, 0, -280, 33.32],
[0, 0, 0, 0, 12]]
self.check_read(_general_example, a,
(5, 5, 8, 'coordinate', 'real', 'general'))
def test_read_hermitian(self):
a = [[1, 0, 0, 0, 0],
[0, 10.5, 0, 250.5 - 22.22j, 0],
[0, 0, .015, 0, 0],
[0, 250.5 + 22.22j, 0, -280, -33.32j],
[0, 0, 0, 33.32j, 12]]
self.check_read(_hermitian_example, a,
(5, 5, 7, 'coordinate', 'complex', 'hermitian'))
def test_read_skew(self):
a = [[1, 0, 0, 0, 0],
[0, 10.5, 0, -250.5, 0],
[0, 0, .015, 0, 0],
[0, 250.5, 0, -280, 0],
[0, 0, 0, 0, 12]]
self.check_read(_skew_example, a,
(5, 5, 7, 'coordinate', 'real', 'skew-symmetric'))
def test_read_symmetric(self):
a = [[1, 0, 0, 0, 0],
[0, 10.5, 0, 250.5, 0],
[0, 0, .015, 0, 0],
[0, 250.5, 0, -280, 8],
[0, 0, 0, 8, 12]]
self.check_read(_symmetric_example, a,
(5, 5, 7, 'coordinate', 'real', 'symmetric'))
def test_read_symmetric_pattern(self):
a = [[1, 0, 0, 0, 0],
[0, 1, 0, 1, 0],
[0, 0, 1, 0, 0],
[0, 1, 0, 1, 1],
[0, 0, 0, 1, 1]]
self.check_read(_symmetric_pattern_example, a,
(5, 5, 7, 'coordinate', 'pattern', 'symmetric'))
def test_empty_write_read(self):
# http://projects.scipy.org/scipy/ticket/883
b = scipy.sparse.coo_matrix((10, 10))
mmwrite(self.fn, b)
assert_equal(mminfo(self.fn),
(10, 10, 0, 'coordinate', 'real', 'symmetric'))
a = b.todense()
b = mmread(self.fn).todense()
assert_array_almost_equal(a, b)
def test_bzip2_py3(self):
# test if fix for #2152 works
try:
# bz2 module isn't always built when building Python.
import bz2
except:
return
I = array([0, 0, 1, 2, 3, 3, 3, 4])
J = array([0, 3, 1, 2, 1, 3, 4, 4])
V = array([1.0, 6.0, 10.5, 0.015, 250.5, -280.0, 33.32, 12.0])
b = scipy.sparse.coo_matrix((V, (I, J)), shape=(5, 5))
mmwrite(self.fn, b)
fn_bzip2 = "%s.bz2" % self.fn
with open(self.fn, 'rb') as f_in:
f_out = bz2.BZ2File(fn_bzip2, 'wb')
f_out.write(f_in.read())
f_out.close()
a = mmread(fn_bzip2).todense()
assert_array_almost_equal(a, b.todense())
def test_gzip_py3(self):
# test if fix for #2152 works
try:
# gzip module can be missing from Python installation
import gzip
except:
return
I = array([0, 0, 1, 2, 3, 3, 3, 4])
J = array([0, 3, 1, 2, 1, 3, 4, 4])
V = array([1.0, 6.0, 10.5, 0.015, 250.5, -280.0, 33.32, 12.0])
b = scipy.sparse.coo_matrix((V, (I, J)), shape=(5, 5))
mmwrite(self.fn, b)
fn_gzip = "%s.gz" % self.fn
with open(self.fn, 'rb') as f_in:
f_out = gzip.open(fn_gzip, 'wb')
f_out.write(f_in.read())
f_out.close()
a = mmread(fn_gzip).todense()
assert_array_almost_equal(a, b.todense())
def test_real_write_read(self):
I = array([0, 0, 1, 2, 3, 3, 3, 4])
J = array([0, 3, 1, 2, 1, 3, 4, 4])
V = array([1.0, 6.0, 10.5, 0.015, 250.5, -280.0, 33.32, 12.0])
b = scipy.sparse.coo_matrix((V, (I, J)), shape=(5, 5))
mmwrite(self.fn, b)
assert_equal(mminfo(self.fn),
(5, 5, 8, 'coordinate', 'real', 'general'))
a = b.todense()
b = mmread(self.fn).todense()
assert_array_almost_equal(a, b)
def test_complex_write_read(self):
I = array([0, 0, 1, 2, 3, 3, 3, 4])
J = array([0, 3, 1, 2, 1, 3, 4, 4])
V = array([1.0 + 3j, 6.0 + 2j, 10.50 + 0.9j, 0.015 + -4.4j,
250.5 + 0j, -280.0 + 5j, 33.32 + 6.4j, 12.00 + 0.8j])
b = scipy.sparse.coo_matrix((V, (I, J)), shape=(5, 5))
mmwrite(self.fn, b)
assert_equal(mminfo(self.fn),
(5, 5, 8, 'coordinate', 'complex', 'general'))
a = b.todense()
b = mmread(self.fn).todense()
assert_array_almost_equal(a, b)
def test_sparse_formats(self):
mats = []
I = array([0, 0, 1, 2, 3, 3, 3, 4])
J = array([0, 3, 1, 2, 1, 3, 4, 4])
V = array([1.0, 6.0, 10.5, 0.015, 250.5, -280.0, 33.32, 12.0])
mats.append(scipy.sparse.coo_matrix((V, (I, J)), shape=(5, 5)))
V = array([1.0 + 3j, 6.0 + 2j, 10.50 + 0.9j, 0.015 + -4.4j,
250.5 + 0j, -280.0 + 5j, 33.32 + 6.4j, 12.00 + 0.8j])
mats.append(scipy.sparse.coo_matrix((V, (I, J)), shape=(5, 5)))
for mat in mats:
expected = mat.todense()
for fmt in ['csr', 'csc', 'coo']:
fn = mktemp(dir=self.tmpdir) # safe, we own tmpdir
mmwrite(fn, mat.asformat(fmt))
result = mmread(fn).todense()
assert_array_almost_equal(result, expected)
def test_precision(self):
test_values = [pi] + [10**(i) for i in range(0, -10, -1)]
test_precisions = range(1, 10)
for value in test_values:
for precision in test_precisions:
# construct sparse matrix with test value at last main diagonal
n = 10**precision + 1
A = scipy.sparse.dok_matrix((n, n))
A[n-1, n-1] = value
# write matrix with test precision and read again
mmwrite(self.fn, A, precision=precision)
A = scipy.io.mmread(self.fn)
# check for right entries in matrix
assert_array_equal(A.row, [n-1])
assert_array_equal(A.col, [n-1])
assert_array_almost_equal(A.data,
[float('%%.%dg' % precision % value)])
| 23,724 | 34.200297 | 86 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/_build_utils/_fortran.py
|
import re
import sys
import os
import glob
from distutils.dep_util import newer
__all__ = ['needs_g77_abi_wrapper', 'split_fortran_files',
'get_g77_abi_wrappers',
'needs_sgemv_fix', 'get_sgemv_fix']
def uses_veclib(info):
if sys.platform != "darwin":
return False
r_accelerate = re.compile("vecLib")
extra_link_args = info.get('extra_link_args', '')
for arg in extra_link_args:
if r_accelerate.search(arg):
return True
return False
def uses_accelerate(info):
if sys.platform != "darwin":
return False
r_accelerate = re.compile("Accelerate")
extra_link_args = info.get('extra_link_args', '')
for arg in extra_link_args:
if r_accelerate.search(arg):
return True
return False
def uses_mkl(info):
r_mkl = re.compile("mkl")
libraries = info.get('libraries', '')
for library in libraries:
if r_mkl.search(library):
return True
return False
def needs_g77_abi_wrapper(info):
"""Returns True if g77 ABI wrapper must be used."""
if uses_accelerate(info) or uses_veclib(info):
return True
elif uses_mkl(info):
return True
else:
return False
def get_g77_abi_wrappers(info):
"""
Returns file names of source files containing Fortran ABI wrapper
routines.
"""
wrapper_sources = []
path = os.path.abspath(os.path.dirname(__file__))
if needs_g77_abi_wrapper(info):
wrapper_sources += [
os.path.join(path, 'src', 'wrap_g77_abi_f.f'),
os.path.join(path, 'src', 'wrap_g77_abi_c.c'),
]
if uses_accelerate(info):
wrapper_sources += [
os.path.join(path, 'src', 'wrap_accelerate_c.c'),
os.path.join(path, 'src', 'wrap_accelerate_f.f'),
]
elif uses_mkl(info):
wrapper_sources += [
os.path.join(path, 'src', 'wrap_dummy_accelerate.f'),
]
else:
raise NotImplementedError("Do not know how to handle LAPACK %s on mac os x" % (info,))
else:
wrapper_sources += [
os.path.join(path, 'src', 'wrap_dummy_g77_abi.f'),
os.path.join(path, 'src', 'wrap_dummy_accelerate.f'),
]
return wrapper_sources
def needs_sgemv_fix(info):
"""Returns True if SGEMV must be fixed."""
if uses_accelerate(info):
return True
else:
return False
def get_sgemv_fix(info):
""" Returns source file needed to correct SGEMV """
path = os.path.abspath(os.path.dirname(__file__))
if needs_sgemv_fix(info):
return [os.path.join(path, 'src', 'apple_sgemv_fix.c')]
else:
return []
def split_fortran_files(source_dir, subroutines=None):
"""Split each file in `source_dir` into separate files per subroutine.
Parameters
----------
source_dir : str
Full path to directory in which sources to be split are located.
subroutines : list of str, optional
Subroutines to split. (Default: all)
Returns
-------
fnames : list of str
List of file names (not including any path) that were created
in `source_dir`.
Notes
-----
This function is useful for code that can't be compiled with g77 because of
type casting errors which do work with gfortran.
Created files are named: ``original_name + '_subr_i' + '.f'``, with ``i``
starting at zero and ending at ``num_subroutines_in_file - 1``.
"""
if subroutines is not None:
subroutines = [x.lower() for x in subroutines]
def split_file(fname):
with open(fname, 'rb') as f:
lines = f.readlines()
subs = []
need_split_next = True
# find lines with SUBROUTINE statements
for ix, line in enumerate(lines):
m = re.match(b'^\\s+subroutine\\s+([a-z0-9_]+)\\s*\\(', line, re.I)
if m and line[0] not in b'Cc!*':
if subroutines is not None:
subr_name = m.group(1).decode('ascii').lower()
subr_wanted = (subr_name in subroutines)
else:
subr_wanted = True
if subr_wanted or need_split_next:
need_split_next = subr_wanted
subs.append(ix)
# check if no split needed
if len(subs) <= 1:
return [fname]
# write out one file per subroutine
new_fnames = []
num_files = len(subs)
for nfile in range(num_files):
new_fname = fname[:-2] + '_subr_' + str(nfile) + '.f'
new_fnames.append(new_fname)
if not newer(fname, new_fname):
continue
with open(new_fname, 'wb') as fn:
if nfile + 1 == num_files:
fn.writelines(lines[subs[nfile]:])
else:
fn.writelines(lines[subs[nfile]:subs[nfile+1]])
return new_fnames
exclude_pattern = re.compile('_subr_[0-9]')
source_fnames = [f for f in glob.glob(os.path.join(source_dir, '*.f'))
if not exclude_pattern.search(os.path.basename(f))]
fnames = []
for source_fname in source_fnames:
created_files = split_file(source_fname)
if created_files is not None:
for cfile in created_files:
fnames.append(os.path.basename(cfile))
return fnames
| 5,612 | 29.672131 | 98 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/_build_utils/__init__.py
|
import numpy as np
from ._fortran import *
from scipy._lib._version import NumpyVersion
# Don't use deprecated Numpy C API. Define this to a fixed version instead of
# NPY_API_VERSION in order not to break compilation for released Scipy versions
# when Numpy introduces a new deprecation. Use in setup.py::
#
# config.add_extension('_name', sources=['source_fname'], **numpy_nodepr_api)
#
if NumpyVersion(np.__version__) >= '1.10.0.dev':
numpy_nodepr_api = dict(define_macros=[("NPY_NO_DEPRECATED_API",
"NPY_1_9_API_VERSION")])
else:
numpy_nodepr_api = dict()
from scipy._lib._testutils import PytestTester
test = PytestTester(__name__)
del PytestTester
| 714 | 31.5 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_differentialevolution.py
|
"""
differential_evolution: The differential evolution global optimization algorithm
Added by Andrew Nelson 2014
"""
from __future__ import division, print_function, absolute_import
import numpy as np
from scipy.optimize import OptimizeResult, minimize
from scipy.optimize.optimize import _status_message
from scipy._lib._util import check_random_state
from scipy._lib.six import xrange, string_types
import warnings
__all__ = ['differential_evolution']
_MACHEPS = np.finfo(np.float64).eps
def differential_evolution(func, bounds, args=(), strategy='best1bin',
maxiter=1000, popsize=15, tol=0.01,
mutation=(0.5, 1), recombination=0.7, seed=None,
callback=None, disp=False, polish=True,
init='latinhypercube', atol=0):
"""Finds the global minimum of a multivariate function.
Differential Evolution is stochastic in nature (does not use gradient
methods) to find the minimium, and can search large areas of candidate
space, but often requires larger numbers of function evaluations than
conventional gradient based techniques.
The algorithm is due to Storn and Price [1]_.
Parameters
----------
func : callable
The objective function to be minimized. Must be in the form
``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
and ``args`` is a tuple of any additional fixed parameters needed to
completely specify the function.
bounds : sequence
Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
defining the lower and upper bounds for the optimizing argument of
`func`. It is required to have ``len(bounds) == len(x)``.
``len(bounds)`` is used to determine the number of parameters in ``x``.
args : tuple, optional
Any additional fixed parameters needed to
completely specify the objective function.
strategy : str, optional
The differential evolution strategy to use. Should be one of:
- 'best1bin'
- 'best1exp'
- 'rand1exp'
- 'randtobest1exp'
- 'currenttobest1exp'
- 'best2exp'
- 'rand2exp'
- 'randtobest1bin'
- 'currenttobest1bin'
- 'best2bin'
- 'rand2bin'
- 'rand1bin'
The default is 'best1bin'.
maxiter : int, optional
The maximum number of generations over which the entire population is
evolved. The maximum number of function evaluations (with no polishing)
is: ``(maxiter + 1) * popsize * len(x)``
popsize : int, optional
A multiplier for setting the total population size. The population has
``popsize * len(x)`` individuals (unless the initial population is
supplied via the `init` keyword).
tol : float, optional
Relative tolerance for convergence, the solving stops when
``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
where and `atol` and `tol` are the absolute and relative tolerance
respectively.
mutation : float or tuple(float, float), optional
The mutation constant. In the literature this is also known as
differential weight, being denoted by F.
If specified as a float it should be in the range [0, 2].
If specified as a tuple ``(min, max)`` dithering is employed. Dithering
randomly changes the mutation constant on a generation by generation
basis. The mutation constant for that generation is taken from
``U[min, max)``. Dithering can help speed convergence significantly.
Increasing the mutation constant increases the search radius, but will
slow down convergence.
recombination : float, optional
The recombination constant, should be in the range [0, 1]. In the
literature this is also known as the crossover probability, being
denoted by CR. Increasing this value allows a larger number of mutants
to progress into the next generation, but at the risk of population
stability.
seed : int or `np.random.RandomState`, optional
If `seed` is not specified the `np.RandomState` singleton is used.
If `seed` is an int, a new `np.random.RandomState` instance is used,
seeded with seed.
If `seed` is already a `np.random.RandomState instance`, then that
`np.random.RandomState` instance is used.
Specify `seed` for repeatable minimizations.
disp : bool, optional
Display status messages
callback : callable, `callback(xk, convergence=val)`, optional
A function to follow the progress of the minimization. ``xk`` is
the current value of ``x0``. ``val`` represents the fractional
value of the population convergence. When ``val`` is greater than one
the function halts. If callback returns `True`, then the minimization
is halted (any polishing is still carried out).
polish : bool, optional
If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B`
method is used to polish the best population member at the end, which
can improve the minimization slightly.
init : str or array-like, optional
Specify which type of population initialization is performed. Should be
one of:
- 'latinhypercube'
- 'random'
- array specifying the initial population. The array should have
shape ``(M, len(x))``, where len(x) is the number of parameters.
`init` is clipped to `bounds` before use.
The default is 'latinhypercube'. Latin Hypercube sampling tries to
maximize coverage of the available parameter space. 'random'
initializes the population randomly - this has the drawback that
clustering can occur, preventing the whole of parameter space being
covered. Use of an array to specify a population subset could be used,
for example, to create a tight bunch of initial guesses in an location
where the solution is known to exist, thereby reducing time for
convergence.
atol : float, optional
Absolute tolerance for convergence, the solving stops when
``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
where and `atol` and `tol` are the absolute and relative tolerance
respectively.
Returns
-------
res : OptimizeResult
The optimization result represented as a `OptimizeResult` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. See
`OptimizeResult` for a description of other attributes. If `polish`
was employed, and a lower minimum was obtained by the polishing, then
OptimizeResult also contains the ``jac`` attribute.
Notes
-----
Differential evolution is a stochastic population based method that is
useful for global optimization problems. At each pass through the population
the algorithm mutates each candidate solution by mixing with other candidate
solutions to create a trial candidate. There are several strategies [2]_ for
creating trial candidates, which suit some problems more than others. The
'best1bin' strategy is a good starting point for many systems. In this
strategy two members of the population are randomly chosen. Their difference
is used to mutate the best member (the `best` in `best1bin`), :math:`b_0`,
so far:
.. math::
b' = b_0 + mutation * (population[rand0] - population[rand1])
A trial vector is then constructed. Starting with a randomly chosen 'i'th
parameter the trial is sequentially filled (in modulo) with parameters from
`b'` or the original candidate. The choice of whether to use `b'` or the
original candidate is made with a binomial distribution (the 'bin' in
'best1bin') - a random number in [0, 1) is generated. If this number is
less than the `recombination` constant then the parameter is loaded from
`b'`, otherwise it is loaded from the original candidate. The final
parameter is always loaded from `b'`. Once the trial candidate is built
its fitness is assessed. If the trial is better than the original candidate
then it takes its place. If it is also better than the best overall
candidate it also replaces that.
To improve your chances of finding a global minimum use higher `popsize`
values, with higher `mutation` and (dithering), but lower `recombination`
values. This has the effect of widening the search radius, but slowing
convergence.
.. versionadded:: 0.15.0
Examples
--------
Let us consider the problem of minimizing the Rosenbrock function. This
function is implemented in `rosen` in `scipy.optimize`.
>>> from scipy.optimize import rosen, differential_evolution
>>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)]
>>> result = differential_evolution(rosen, bounds)
>>> result.x, result.fun
(array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19)
Next find the minimum of the Ackley function
(http://en.wikipedia.org/wiki/Test_functions_for_optimization).
>>> from scipy.optimize import differential_evolution
>>> import numpy as np
>>> def ackley(x):
... arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2))
... arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1]))
... return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e
>>> bounds = [(-5, 5), (-5, 5)]
>>> result = differential_evolution(ackley, bounds)
>>> result.x, result.fun
(array([ 0., 0.]), 4.4408920985006262e-16)
References
----------
.. [1] Storn, R and Price, K, Differential Evolution - a Simple and
Efficient Heuristic for Global Optimization over Continuous Spaces,
Journal of Global Optimization, 1997, 11, 341 - 359.
.. [2] http://www1.icsi.berkeley.edu/~storn/code.html
.. [3] http://en.wikipedia.org/wiki/Differential_evolution
"""
solver = DifferentialEvolutionSolver(func, bounds, args=args,
strategy=strategy, maxiter=maxiter,
popsize=popsize, tol=tol,
mutation=mutation,
recombination=recombination,
seed=seed, polish=polish,
callback=callback,
disp=disp, init=init, atol=atol)
return solver.solve()
class DifferentialEvolutionSolver(object):
"""This class implements the differential evolution solver
Parameters
----------
func : callable
The objective function to be minimized. Must be in the form
``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
and ``args`` is a tuple of any additional fixed parameters needed to
completely specify the function.
bounds : sequence
Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
defining the lower and upper bounds for the optimizing argument of
`func`. It is required to have ``len(bounds) == len(x)``.
``len(bounds)`` is used to determine the number of parameters in ``x``.
args : tuple, optional
Any additional fixed parameters needed to
completely specify the objective function.
strategy : str, optional
The differential evolution strategy to use. Should be one of:
- 'best1bin'
- 'best1exp'
- 'rand1exp'
- 'randtobest1exp'
- 'currenttobest1exp'
- 'best2exp'
- 'rand2exp'
- 'randtobest1bin'
- 'currenttobest1bin'
- 'best2bin'
- 'rand2bin'
- 'rand1bin'
The default is 'best1bin'
maxiter : int, optional
The maximum number of generations over which the entire population is
evolved. The maximum number of function evaluations (with no polishing)
is: ``(maxiter + 1) * popsize * len(x)``
popsize : int, optional
A multiplier for setting the total population size. The population has
``popsize * len(x)`` individuals (unless the initial population is
supplied via the `init` keyword).
tol : float, optional
Relative tolerance for convergence, the solving stops when
``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
where and `atol` and `tol` are the absolute and relative tolerance
respectively.
mutation : float or tuple(float, float), optional
The mutation constant. In the literature this is also known as
differential weight, being denoted by F.
If specified as a float it should be in the range [0, 2].
If specified as a tuple ``(min, max)`` dithering is employed. Dithering
randomly changes the mutation constant on a generation by generation
basis. The mutation constant for that generation is taken from
U[min, max). Dithering can help speed convergence significantly.
Increasing the mutation constant increases the search radius, but will
slow down convergence.
recombination : float, optional
The recombination constant, should be in the range [0, 1]. In the
literature this is also known as the crossover probability, being
denoted by CR. Increasing this value allows a larger number of mutants
to progress into the next generation, but at the risk of population
stability.
seed : int or `np.random.RandomState`, optional
If `seed` is not specified the `np.random.RandomState` singleton is
used.
If `seed` is an int, a new `np.random.RandomState` instance is used,
seeded with `seed`.
If `seed` is already a `np.random.RandomState` instance, then that
`np.random.RandomState` instance is used.
Specify `seed` for repeatable minimizations.
disp : bool, optional
Display status messages
callback : callable, `callback(xk, convergence=val)`, optional
A function to follow the progress of the minimization. ``xk`` is
the current value of ``x0``. ``val`` represents the fractional
value of the population convergence. When ``val`` is greater than one
the function halts. If callback returns `True`, then the minimization
is halted (any polishing is still carried out).
polish : bool, optional
If True, then `scipy.optimize.minimize` with the `L-BFGS-B` method
is used to polish the best population member at the end. This requires
a few more function evaluations.
maxfun : int, optional
Set the maximum number of function evaluations. However, it probably
makes more sense to set `maxiter` instead.
init : str or array-like, optional
Specify which type of population initialization is performed. Should be
one of:
- 'latinhypercube'
- 'random'
- array specifying the initial population. The array should have
shape ``(M, len(x))``, where len(x) is the number of parameters.
`init` is clipped to `bounds` before use.
The default is 'latinhypercube'. Latin Hypercube sampling tries to
maximize coverage of the available parameter space. 'random'
initializes the population randomly - this has the drawback that
clustering can occur, preventing the whole of parameter space being
covered. Use of an array to specify a population could be used, for
example, to create a tight bunch of initial guesses in an location
where the solution is known to exist, thereby reducing time for
convergence.
atol : float, optional
Absolute tolerance for convergence, the solving stops when
``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
where and `atol` and `tol` are the absolute and relative tolerance
respectively.
"""
# Dispatch of mutation strategy method (binomial or exponential).
_binomial = {'best1bin': '_best1',
'randtobest1bin': '_randtobest1',
'currenttobest1bin': '_currenttobest1',
'best2bin': '_best2',
'rand2bin': '_rand2',
'rand1bin': '_rand1'}
_exponential = {'best1exp': '_best1',
'rand1exp': '_rand1',
'randtobest1exp': '_randtobest1',
'currenttobest1exp': '_currenttobest1',
'best2exp': '_best2',
'rand2exp': '_rand2'}
__init_error_msg = ("The population initialization method must be one of "
"'latinhypercube' or 'random', or an array of shape "
"(M, N) where N is the number of parameters and M>5")
def __init__(self, func, bounds, args=(),
strategy='best1bin', maxiter=1000, popsize=15,
tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None,
maxfun=np.inf, callback=None, disp=False, polish=True,
init='latinhypercube', atol=0):
if strategy in self._binomial:
self.mutation_func = getattr(self, self._binomial[strategy])
elif strategy in self._exponential:
self.mutation_func = getattr(self, self._exponential[strategy])
else:
raise ValueError("Please select a valid mutation strategy")
self.strategy = strategy
self.callback = callback
self.polish = polish
# relative and absolute tolerances for convergence
self.tol, self.atol = tol, atol
# Mutation constant should be in [0, 2). If specified as a sequence
# then dithering is performed.
self.scale = mutation
if (not np.all(np.isfinite(mutation)) or
np.any(np.array(mutation) >= 2) or
np.any(np.array(mutation) < 0)):
raise ValueError('The mutation constant must be a float in '
'U[0, 2), or specified as a tuple(min, max)'
' where min < max and min, max are in U[0, 2).')
self.dither = None
if hasattr(mutation, '__iter__') and len(mutation) > 1:
self.dither = [mutation[0], mutation[1]]
self.dither.sort()
self.cross_over_probability = recombination
self.func = func
self.args = args
# convert tuple of lower and upper bounds to limits
# [(low_0, high_0), ..., (low_n, high_n]
# -> [[low_0, ..., low_n], [high_0, ..., high_n]]
self.limits = np.array(bounds, dtype='float').T
if (np.size(self.limits, 0) != 2 or not
np.all(np.isfinite(self.limits))):
raise ValueError('bounds should be a sequence containing '
'real valued (min, max) pairs for each value'
' in x')
if maxiter is None: # the default used to be None
maxiter = 1000
self.maxiter = maxiter
if maxfun is None: # the default used to be None
maxfun = np.inf
self.maxfun = maxfun
# population is scaled to between [0, 1].
# We have to scale between parameter <-> population
# save these arguments for _scale_parameter and
# _unscale_parameter. This is an optimization
self.__scale_arg1 = 0.5 * (self.limits[0] + self.limits[1])
self.__scale_arg2 = np.fabs(self.limits[0] - self.limits[1])
self.parameter_count = np.size(self.limits, 1)
self.random_number_generator = check_random_state(seed)
# default population initialization is a latin hypercube design, but
# there are other population initializations possible.
# the minimum is 5 because 'best2bin' requires a population that's at
# least 5 long
self.num_population_members = max(5, popsize * self.parameter_count)
self.population_shape = (self.num_population_members,
self.parameter_count)
self._nfev = 0
if isinstance(init, string_types):
if init == 'latinhypercube':
self.init_population_lhs()
elif init == 'random':
self.init_population_random()
else:
raise ValueError(self.__init_error_msg)
else:
self.init_population_array(init)
self.disp = disp
def init_population_lhs(self):
"""
Initializes the population with Latin Hypercube Sampling.
Latin Hypercube Sampling ensures that each parameter is uniformly
sampled over its range.
"""
rng = self.random_number_generator
# Each parameter range needs to be sampled uniformly. The scaled
# parameter range ([0, 1)) needs to be split into
# `self.num_population_members` segments, each of which has the following
# size:
segsize = 1.0 / self.num_population_members
# Within each segment we sample from a uniform random distribution.
# We need to do this sampling for each parameter.
samples = (segsize * rng.random_sample(self.population_shape)
# Offset each segment to cover the entire parameter range [0, 1)
+ np.linspace(0., 1., self.num_population_members,
endpoint=False)[:, np.newaxis])
# Create an array for population of candidate solutions.
self.population = np.zeros_like(samples)
# Initialize population of candidate solutions by permutation of the
# random samples.
for j in range(self.parameter_count):
order = rng.permutation(range(self.num_population_members))
self.population[:, j] = samples[order, j]
# reset population energies
self.population_energies = (np.ones(self.num_population_members) *
np.inf)
# reset number of function evaluations counter
self._nfev = 0
def init_population_random(self):
"""
Initialises the population at random. This type of initialization
can possess clustering, Latin Hypercube sampling is generally better.
"""
rng = self.random_number_generator
self.population = rng.random_sample(self.population_shape)
# reset population energies
self.population_energies = (np.ones(self.num_population_members) *
np.inf)
# reset number of function evaluations counter
self._nfev = 0
def init_population_array(self, init):
"""
Initialises the population with a user specified population.
Parameters
----------
init : np.ndarray
Array specifying subset of the initial population. The array should
have shape (M, len(x)), where len(x) is the number of parameters.
The population is clipped to the lower and upper `bounds`.
"""
# make sure you're using a float array
popn = np.asfarray(init)
if (np.size(popn, 0) < 5 or
popn.shape[1] != self.parameter_count or
len(popn.shape) != 2):
raise ValueError("The population supplied needs to have shape"
" (M, len(x)), where M > 4.")
# scale values and clip to bounds, assigning to population
self.population = np.clip(self._unscale_parameters(popn), 0, 1)
self.num_population_members = np.size(self.population, 0)
self.population_shape = (self.num_population_members,
self.parameter_count)
# reset population energies
self.population_energies = (np.ones(self.num_population_members) *
np.inf)
# reset number of function evaluations counter
self._nfev = 0
@property
def x(self):
"""
The best solution from the solver
Returns
-------
x : ndarray
The best solution from the solver.
"""
return self._scale_parameters(self.population[0])
@property
def convergence(self):
"""
The standard deviation of the population energies divided by their
mean.
"""
return (np.std(self.population_energies) /
np.abs(np.mean(self.population_energies) + _MACHEPS))
def solve(self):
"""
Runs the DifferentialEvolutionSolver.
Returns
-------
res : OptimizeResult
The optimization result represented as a ``OptimizeResult`` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. See
`OptimizeResult` for a description of other attributes. If `polish`
was employed, and a lower minimum was obtained by the polishing,
then OptimizeResult also contains the ``jac`` attribute.
"""
nit, warning_flag = 0, False
status_message = _status_message['success']
# The population may have just been initialized (all entries are
# np.inf). If it has you have to calculate the initial energies.
# Although this is also done in the evolve generator it's possible
# that someone can set maxiter=0, at which point we still want the
# initial energies to be calculated (the following loop isn't run).
if np.all(np.isinf(self.population_energies)):
self._calculate_population_energies()
# do the optimisation.
for nit in xrange(1, self.maxiter + 1):
# evolve the population by a generation
try:
next(self)
except StopIteration:
warning_flag = True
status_message = _status_message['maxfev']
break
if self.disp:
print("differential_evolution step %d: f(x)= %g"
% (nit,
self.population_energies[0]))
# should the solver terminate?
convergence = self.convergence
if (self.callback and
self.callback(self._scale_parameters(self.population[0]),
convergence=self.tol / convergence) is True):
warning_flag = True
status_message = ('callback function requested stop early '
'by returning True')
break
intol = (np.std(self.population_energies) <=
self.atol +
self.tol * np.abs(np.mean(self.population_energies)))
if warning_flag or intol:
break
else:
status_message = _status_message['maxiter']
warning_flag = True
DE_result = OptimizeResult(
x=self.x,
fun=self.population_energies[0],
nfev=self._nfev,
nit=nit,
message=status_message,
success=(warning_flag is not True))
if self.polish:
result = minimize(self.func,
np.copy(DE_result.x),
method='L-BFGS-B',
bounds=self.limits.T,
args=self.args)
self._nfev += result.nfev
DE_result.nfev = self._nfev
if result.fun < DE_result.fun:
DE_result.fun = result.fun
DE_result.x = result.x
DE_result.jac = result.jac
# to keep internal state consistent
self.population_energies[0] = result.fun
self.population[0] = self._unscale_parameters(result.x)
return DE_result
def _calculate_population_energies(self):
"""
Calculate the energies of all the population members at the same time.
Puts the best member in first place. Useful if the population has just
been initialised.
"""
for index, candidate in enumerate(self.population):
if self._nfev > self.maxfun:
break
parameters = self._scale_parameters(candidate)
self.population_energies[index] = self.func(parameters,
*self.args)
self._nfev += 1
minval = np.argmin(self.population_energies)
# put the lowest energy into the best solution position.
lowest_energy = self.population_energies[minval]
self.population_energies[minval] = self.population_energies[0]
self.population_energies[0] = lowest_energy
self.population[[0, minval], :] = self.population[[minval, 0], :]
def __iter__(self):
return self
def __next__(self):
"""
Evolve the population by a single generation
Returns
-------
x : ndarray
The best solution from the solver.
fun : float
Value of objective function obtained from the best solution.
"""
# the population may have just been initialized (all entries are
# np.inf). If it has you have to calculate the initial energies
if np.all(np.isinf(self.population_energies)):
self._calculate_population_energies()
if self.dither is not None:
self.scale = (self.random_number_generator.rand()
* (self.dither[1] - self.dither[0]) + self.dither[0])
for candidate in range(self.num_population_members):
if self._nfev > self.maxfun:
raise StopIteration
# create a trial solution
trial = self._mutate(candidate)
# ensuring that it's in the range [0, 1)
self._ensure_constraint(trial)
# scale from [0, 1) to the actual parameter value
parameters = self._scale_parameters(trial)
# determine the energy of the objective function
energy = self.func(parameters, *self.args)
self._nfev += 1
# if the energy of the trial candidate is lower than the
# original population member then replace it
if energy < self.population_energies[candidate]:
self.population[candidate] = trial
self.population_energies[candidate] = energy
# if the trial candidate also has a lower energy than the
# best solution then replace that as well
if energy < self.population_energies[0]:
self.population_energies[0] = energy
self.population[0] = trial
return self.x, self.population_energies[0]
def next(self):
"""
Evolve the population by a single generation
Returns
-------
x : ndarray
The best solution from the solver.
fun : float
Value of objective function obtained from the best solution.
"""
# next() is required for compatibility with Python2.7.
return self.__next__()
def _scale_parameters(self, trial):
"""
scale from a number between 0 and 1 to parameters.
"""
return self.__scale_arg1 + (trial - 0.5) * self.__scale_arg2
def _unscale_parameters(self, parameters):
"""
scale from parameters to a number between 0 and 1.
"""
return (parameters - self.__scale_arg1) / self.__scale_arg2 + 0.5
def _ensure_constraint(self, trial):
"""
make sure the parameters lie between the limits
"""
for index in np.where((trial < 0) | (trial > 1))[0]:
trial[index] = self.random_number_generator.rand()
def _mutate(self, candidate):
"""
create a trial vector based on a mutation strategy
"""
trial = np.copy(self.population[candidate])
rng = self.random_number_generator
fill_point = rng.randint(0, self.parameter_count)
if self.strategy in ['currenttobest1exp', 'currenttobest1bin']:
bprime = self.mutation_func(candidate,
self._select_samples(candidate, 5))
else:
bprime = self.mutation_func(self._select_samples(candidate, 5))
if self.strategy in self._binomial:
crossovers = rng.rand(self.parameter_count)
crossovers = crossovers < self.cross_over_probability
# the last one is always from the bprime vector for binomial
# If you fill in modulo with a loop you have to set the last one to
# true. If you don't use a loop then you can have any random entry
# be True.
crossovers[fill_point] = True
trial = np.where(crossovers, bprime, trial)
return trial
elif self.strategy in self._exponential:
i = 0
while (i < self.parameter_count and
rng.rand() < self.cross_over_probability):
trial[fill_point] = bprime[fill_point]
fill_point = (fill_point + 1) % self.parameter_count
i += 1
return trial
def _best1(self, samples):
"""
best1bin, best1exp
"""
r0, r1 = samples[:2]
return (self.population[0] + self.scale *
(self.population[r0] - self.population[r1]))
def _rand1(self, samples):
"""
rand1bin, rand1exp
"""
r0, r1, r2 = samples[:3]
return (self.population[r0] + self.scale *
(self.population[r1] - self.population[r2]))
def _randtobest1(self, samples):
"""
randtobest1bin, randtobest1exp
"""
r0, r1, r2 = samples[:3]
bprime = np.copy(self.population[r0])
bprime += self.scale * (self.population[0] - bprime)
bprime += self.scale * (self.population[r1] -
self.population[r2])
return bprime
def _currenttobest1(self, candidate, samples):
"""
currenttobest1bin, currenttobest1exp
"""
r0, r1 = samples[:2]
bprime = (self.population[candidate] + self.scale *
(self.population[0] - self.population[candidate] +
self.population[r0] - self.population[r1]))
return bprime
def _best2(self, samples):
"""
best2bin, best2exp
"""
r0, r1, r2, r3 = samples[:4]
bprime = (self.population[0] + self.scale *
(self.population[r0] + self.population[r1] -
self.population[r2] - self.population[r3]))
return bprime
def _rand2(self, samples):
"""
rand2bin, rand2exp
"""
r0, r1, r2, r3, r4 = samples
bprime = (self.population[r0] + self.scale *
(self.population[r1] + self.population[r2] -
self.population[r3] - self.population[r4]))
return bprime
def _select_samples(self, candidate, number_samples):
"""
obtain random integers from range(self.num_population_members),
without replacement. You can't have the original candidate either.
"""
idxs = list(range(self.num_population_members))
idxs.remove(candidate)
self.random_number_generator.shuffle(idxs)
idxs = idxs[:number_samples]
return idxs
| 36,263 | 40.82699 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/lbfgsb.py
|
"""
Functions
---------
.. autosummary::
:toctree: generated/
fmin_l_bfgs_b
"""
## License for the Python wrapper
## ==============================
## Copyright (c) 2004 David M. Cooke <cookedm@physics.mcmaster.ca>
## Permission is hereby granted, free of charge, to any person obtaining a
## copy of this software and associated documentation files (the "Software"),
## to deal in the Software without restriction, including without limitation
## the rights to use, copy, modify, merge, publish, distribute, sublicense,
## and/or sell copies of the Software, and to permit persons to whom the
## Software is furnished to do so, subject to the following conditions:
## The above copyright notice and this permission notice shall be included in
## all copies or substantial portions of the Software.
## THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
## IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
## FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
## AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
## LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
## FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
## DEALINGS IN THE SOFTWARE.
## Modifications by Travis Oliphant and Enthought, Inc. for inclusion in SciPy
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy import array, asarray, float64, int32, zeros
from . import _lbfgsb
from .optimize import (approx_fprime, MemoizeJac, OptimizeResult,
_check_unknown_options, wrap_function,
_approx_fprime_helper)
from scipy.sparse.linalg import LinearOperator
__all__ = ['fmin_l_bfgs_b', 'LbfgsInvHessProduct']
def fmin_l_bfgs_b(func, x0, fprime=None, args=(),
approx_grad=0,
bounds=None, m=10, factr=1e7, pgtol=1e-5,
epsilon=1e-8,
iprint=-1, maxfun=15000, maxiter=15000, disp=None,
callback=None, maxls=20):
"""
Minimize a function func using the L-BFGS-B algorithm.
Parameters
----------
func : callable f(x,*args)
Function to minimise.
x0 : ndarray
Initial guess.
fprime : callable fprime(x,*args), optional
The gradient of `func`. If None, then `func` returns the function
value and the gradient (``f, g = func(x, *args)``), unless
`approx_grad` is True in which case `func` returns only ``f``.
args : sequence, optional
Arguments to pass to `func` and `fprime`.
approx_grad : bool, optional
Whether to approximate the gradient numerically (in which case
`func` returns only the function value).
bounds : list, optional
``(min, max)`` pairs for each element in ``x``, defining
the bounds on that parameter. Use None or +-inf for one of ``min`` or
``max`` when there is no bound in that direction.
m : int, optional
The maximum number of variable metric corrections
used to define the limited memory matrix. (The limited memory BFGS
method does not store the full hessian but uses this many terms in an
approximation to it.)
factr : float, optional
The iteration stops when
``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps``,
where ``eps`` is the machine precision, which is automatically
generated by the code. Typical values for `factr` are: 1e12 for
low accuracy; 1e7 for moderate accuracy; 10.0 for extremely
high accuracy. See Notes for relationship to `ftol`, which is exposed
(instead of `factr`) by the `scipy.optimize.minimize` interface to
L-BFGS-B.
pgtol : float, optional
The iteration will stop when
``max{|proj g_i | i = 1, ..., n} <= pgtol``
where ``pg_i`` is the i-th component of the projected gradient.
epsilon : float, optional
Step size used when `approx_grad` is True, for numerically
calculating the gradient
iprint : int, optional
Controls the frequency of output. ``iprint < 0`` means no output;
``iprint = 0`` print only one line at the last iteration;
``0 < iprint < 99`` print also f and ``|proj g|`` every iprint iterations;
``iprint = 99`` print details of every iteration except n-vectors;
``iprint = 100`` print also the changes of active set and final x;
``iprint > 100`` print details of every iteration including x and g.
disp : int, optional
If zero, then no output. If a positive number, then this over-rides
`iprint` (i.e., `iprint` gets the value of `disp`).
maxfun : int, optional
Maximum number of function evaluations.
maxiter : int, optional
Maximum number of iterations.
callback : callable, optional
Called after each iteration, as ``callback(xk)``, where ``xk`` is the
current parameter vector.
maxls : int, optional
Maximum number of line search steps (per iteration). Default is 20.
Returns
-------
x : array_like
Estimated position of the minimum.
f : float
Value of `func` at the minimum.
d : dict
Information dictionary.
* d['warnflag'] is
- 0 if converged,
- 1 if too many function evaluations or too many iterations,
- 2 if stopped for another reason, given in d['task']
* d['grad'] is the gradient at the minimum (should be 0 ish)
* d['funcalls'] is the number of function calls made.
* d['nit'] is the number of iterations.
See also
--------
minimize: Interface to minimization algorithms for multivariate
functions. See the 'L-BFGS-B' `method` in particular. Note that the
`ftol` option is made available via that interface, while `factr` is
provided via this interface, where `factr` is the factor multiplying
the default machine floating-point precision to arrive at `ftol`:
``ftol = factr * numpy.finfo(float).eps``.
Notes
-----
License of L-BFGS-B (FORTRAN code):
The version included here (in fortran code) is 3.0
(released April 25, 2011). It was written by Ciyou Zhu, Richard Byrd,
and Jorge Nocedal <nocedal@ece.nwu.edu>. It carries the following
condition for use:
This software is freely available, but we expect that all publications
describing work using this software, or all commercial products using it,
quote at least one of the references given below. This software is released
under the BSD License.
References
----------
* R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound
Constrained Optimization, (1995), SIAM Journal on Scientific and
Statistical Computing, 16, 5, pp. 1190-1208.
* C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B,
FORTRAN routines for large scale bound constrained optimization (1997),
ACM Transactions on Mathematical Software, 23, 4, pp. 550 - 560.
* J.L. Morales and J. Nocedal. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B,
FORTRAN routines for large scale bound constrained optimization (2011),
ACM Transactions on Mathematical Software, 38, 1.
"""
# handle fprime/approx_grad
if approx_grad:
fun = func
jac = None
elif fprime is None:
fun = MemoizeJac(func)
jac = fun.derivative
else:
fun = func
jac = fprime
# build options
if disp is None:
disp = iprint
opts = {'disp': disp,
'iprint': iprint,
'maxcor': m,
'ftol': factr * np.finfo(float).eps,
'gtol': pgtol,
'eps': epsilon,
'maxfun': maxfun,
'maxiter': maxiter,
'callback': callback,
'maxls': maxls}
res = _minimize_lbfgsb(fun, x0, args=args, jac=jac, bounds=bounds,
**opts)
d = {'grad': res['jac'],
'task': res['message'],
'funcalls': res['nfev'],
'nit': res['nit'],
'warnflag': res['status']}
f = res['fun']
x = res['x']
return x, f, d
def _minimize_lbfgsb(fun, x0, args=(), jac=None, bounds=None,
disp=None, maxcor=10, ftol=2.2204460492503131e-09,
gtol=1e-5, eps=1e-8, maxfun=15000, maxiter=15000,
iprint=-1, callback=None, maxls=20, **unknown_options):
"""
Minimize a scalar function of one or more variables using the L-BFGS-B
algorithm.
Options
-------
disp : bool
Set to True to print convergence messages.
maxcor : int
The maximum number of variable metric corrections used to
define the limited memory matrix. (The limited memory BFGS
method does not store the full hessian but uses this many terms
in an approximation to it.)
ftol : float
The iteration stops when ``(f^k -
f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= ftol``.
gtol : float
The iteration will stop when ``max{|proj g_i | i = 1, ..., n}
<= gtol`` where ``pg_i`` is the i-th component of the
projected gradient.
eps : float
Step size used for numerical approximation of the jacobian.
disp : int
Set to True to print convergence messages.
maxfun : int
Maximum number of function evaluations.
maxiter : int
Maximum number of iterations.
maxls : int, optional
Maximum number of line search steps (per iteration). Default is 20.
Notes
-----
The option `ftol` is exposed via the `scipy.optimize.minimize` interface,
but calling `scipy.optimize.fmin_l_bfgs_b` directly exposes `factr`. The
relationship between the two is ``ftol = factr * numpy.finfo(float).eps``.
I.e., `factr` multiplies the default machine floating-point precision to
arrive at `ftol`.
"""
_check_unknown_options(unknown_options)
m = maxcor
epsilon = eps
pgtol = gtol
factr = ftol / np.finfo(float).eps
x0 = asarray(x0).ravel()
n, = x0.shape
if bounds is None:
bounds = [(None, None)] * n
if len(bounds) != n:
raise ValueError('length of x0 != length of bounds')
# unbounded variables must use None, not +-inf, for optimizer to work properly
bounds = [(None if l == -np.inf else l, None if u == np.inf else u) for l, u in bounds]
if disp is not None:
if disp == 0:
iprint = -1
else:
iprint = disp
n_function_evals, fun = wrap_function(fun, ())
if jac is None:
def func_and_grad(x):
f = fun(x, *args)
g = _approx_fprime_helper(x, fun, epsilon, args=args, f0=f)
return f, g
else:
def func_and_grad(x):
f = fun(x, *args)
g = jac(x, *args)
return f, g
nbd = zeros(n, int32)
low_bnd = zeros(n, float64)
upper_bnd = zeros(n, float64)
bounds_map = {(None, None): 0,
(1, None): 1,
(1, 1): 2,
(None, 1): 3}
for i in range(0, n):
l, u = bounds[i]
if l is not None:
low_bnd[i] = l
l = 1
if u is not None:
upper_bnd[i] = u
u = 1
nbd[i] = bounds_map[l, u]
if not maxls > 0:
raise ValueError('maxls must be positive.')
x = array(x0, float64)
f = array(0.0, float64)
g = zeros((n,), float64)
wa = zeros(2*m*n + 5*n + 11*m*m + 8*m, float64)
iwa = zeros(3*n, int32)
task = zeros(1, 'S60')
csave = zeros(1, 'S60')
lsave = zeros(4, int32)
isave = zeros(44, int32)
dsave = zeros(29, float64)
task[:] = 'START'
n_iterations = 0
while 1:
# x, f, g, wa, iwa, task, csave, lsave, isave, dsave = \
_lbfgsb.setulb(m, x, low_bnd, upper_bnd, nbd, f, g, factr,
pgtol, wa, iwa, task, iprint, csave, lsave,
isave, dsave, maxls)
task_str = task.tostring()
if task_str.startswith(b'FG'):
# The minimization routine wants f and g at the current x.
# Note that interruptions due to maxfun are postponed
# until the completion of the current minimization iteration.
# Overwrite f and g:
f, g = func_and_grad(x)
elif task_str.startswith(b'NEW_X'):
# new iteration
n_iterations += 1
if callback is not None:
callback(np.copy(x))
if n_iterations >= maxiter:
task[:] = 'STOP: TOTAL NO. of ITERATIONS REACHED LIMIT'
elif n_function_evals[0] > maxfun:
task[:] = ('STOP: TOTAL NO. of f AND g EVALUATIONS '
'EXCEEDS LIMIT')
else:
break
task_str = task.tostring().strip(b'\x00').strip()
if task_str.startswith(b'CONV'):
warnflag = 0
elif n_function_evals[0] > maxfun or n_iterations >= maxiter:
warnflag = 1
else:
warnflag = 2
# These two portions of the workspace are described in the mainlb
# subroutine in lbfgsb.f. See line 363.
s = wa[0: m*n].reshape(m, n)
y = wa[m*n: 2*m*n].reshape(m, n)
# See lbfgsb.f line 160 for this portion of the workspace.
# isave(31) = the total number of BFGS updates prior the current iteration;
n_bfgs_updates = isave[30]
n_corrs = min(n_bfgs_updates, maxcor)
hess_inv = LbfgsInvHessProduct(s[:n_corrs], y[:n_corrs])
return OptimizeResult(fun=f, jac=g, nfev=n_function_evals[0],
nit=n_iterations, status=warnflag, message=task_str,
x=x, success=(warnflag == 0), hess_inv=hess_inv)
class LbfgsInvHessProduct(LinearOperator):
"""Linear operator for the L-BFGS approximate inverse Hessian.
This operator computes the product of a vector with the approximate inverse
of the Hessian of the objective function, using the L-BFGS limited
memory approximation to the inverse Hessian, accumulated during the
optimization.
Objects of this class implement the ``scipy.sparse.linalg.LinearOperator``
interface.
Parameters
----------
sk : array_like, shape=(n_corr, n)
Array of `n_corr` most recent updates to the solution vector.
(See [1]).
yk : array_like, shape=(n_corr, n)
Array of `n_corr` most recent updates to the gradient. (See [1]).
References
----------
.. [1] Nocedal, Jorge. "Updating quasi-Newton matrices with limited
storage." Mathematics of computation 35.151 (1980): 773-782.
"""
def __init__(self, sk, yk):
"""Construct the operator."""
if sk.shape != yk.shape or sk.ndim != 2:
raise ValueError('sk and yk must have matching shape, (n_corrs, n)')
n_corrs, n = sk.shape
super(LbfgsInvHessProduct, self).__init__(
dtype=np.float64, shape=(n, n))
self.sk = sk
self.yk = yk
self.n_corrs = n_corrs
self.rho = 1 / np.einsum('ij,ij->i', sk, yk)
def _matvec(self, x):
"""Efficient matrix-vector multiply with the BFGS matrices.
This calculation is described in Section (4) of [1].
Parameters
----------
x : ndarray
An array with shape (n,) or (n,1).
Returns
-------
y : ndarray
The matrix-vector product
"""
s, y, n_corrs, rho = self.sk, self.yk, self.n_corrs, self.rho
q = np.array(x, dtype=self.dtype, copy=True)
if q.ndim == 2 and q.shape[1] == 1:
q = q.reshape(-1)
alpha = np.zeros(n_corrs)
for i in range(n_corrs-1, -1, -1):
alpha[i] = rho[i] * np.dot(s[i], q)
q = q - alpha[i]*y[i]
r = q
for i in range(n_corrs):
beta = rho[i] * np.dot(y[i], r)
r = r + s[i] * (alpha[i] - beta)
return r
def todense(self):
"""Return a dense array representation of this operator.
Returns
-------
arr : ndarray, shape=(n, n)
An array with the same shape and containing
the same data represented by this `LinearOperator`.
"""
s, y, n_corrs, rho = self.sk, self.yk, self.n_corrs, self.rho
I = np.eye(*self.shape, dtype=self.dtype)
Hk = I
for i in range(n_corrs):
A1 = I - s[i][:, np.newaxis] * y[i][np.newaxis, :] * rho[i]
A2 = I - y[i][:, np.newaxis] * s[i][np.newaxis, :] * rho[i]
Hk = np.dot(A1, np.dot(Hk, A2)) + (rho[i] * s[i][:, np.newaxis] *
s[i][np.newaxis, :])
return Hk
| 16,922 | 35.083156 | 91 |
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_trustregion_dogleg.py
|
"""Dog-leg trust-region optimization."""
from __future__ import division, print_function, absolute_import
import numpy as np
import scipy.linalg
from ._trustregion import (_minimize_trust_region, BaseQuadraticSubproblem)
__all__ = []
def _minimize_dogleg(fun, x0, args=(), jac=None, hess=None,
**trust_region_options):
"""
Minimization of scalar function of one or more variables using
the dog-leg trust-region algorithm.
Options
-------
initial_trust_radius : float
Initial trust-region radius.
max_trust_radius : float
Maximum value of the trust-region radius. No steps that are longer
than this value will be proposed.
eta : float
Trust region related acceptance stringency for proposed steps.
gtol : float
Gradient norm must be less than `gtol` before successful
termination.
"""
if jac is None:
raise ValueError('Jacobian is required for dogleg minimization')
if hess is None:
raise ValueError('Hessian is required for dogleg minimization')
return _minimize_trust_region(fun, x0, args=args, jac=jac, hess=hess,
subproblem=DoglegSubproblem,
**trust_region_options)
class DoglegSubproblem(BaseQuadraticSubproblem):
"""Quadratic subproblem solved by the dogleg method"""
def cauchy_point(self):
"""
The Cauchy point is minimal along the direction of steepest descent.
"""
if self._cauchy_point is None:
g = self.jac
Bg = self.hessp(g)
self._cauchy_point = -(np.dot(g, g) / np.dot(g, Bg)) * g
return self._cauchy_point
def newton_point(self):
"""
The Newton point is a global minimum of the approximate function.
"""
if self._newton_point is None:
g = self.jac
B = self.hess
cho_info = scipy.linalg.cho_factor(B)
self._newton_point = -scipy.linalg.cho_solve(cho_info, g)
return self._newton_point
def solve(self, trust_radius):
"""
Minimize a function using the dog-leg trust-region algorithm.
This algorithm requires function values and first and second derivatives.
It also performs a costly Hessian decomposition for most iterations,
and the Hessian is required to be positive definite.
Parameters
----------
trust_radius : float
We are allowed to wander only this far away from the origin.
Returns
-------
p : ndarray
The proposed step.
hits_boundary : bool
True if the proposed step is on the boundary of the trust region.
Notes
-----
The Hessian is required to be positive definite.
References
----------
.. [1] Jorge Nocedal and Stephen Wright,
Numerical Optimization, second edition,
Springer-Verlag, 2006, page 73.
"""
# Compute the Newton point.
# This is the optimum for the quadratic model function.
# If it is inside the trust radius then return this point.
p_best = self.newton_point()
if scipy.linalg.norm(p_best) < trust_radius:
hits_boundary = False
return p_best, hits_boundary
# Compute the Cauchy point.
# This is the predicted optimum along the direction of steepest descent.
p_u = self.cauchy_point()
# If the Cauchy point is outside the trust region,
# then return the point where the path intersects the boundary.
p_u_norm = scipy.linalg.norm(p_u)
if p_u_norm >= trust_radius:
p_boundary = p_u * (trust_radius / p_u_norm)
hits_boundary = True
return p_boundary, hits_boundary
# Compute the intersection of the trust region boundary
# and the line segment connecting the Cauchy and Newton points.
# This requires solving a quadratic equation.
# ||p_u + t*(p_best - p_u)||**2 == trust_radius**2
# Solve this for positive time t using the quadratic formula.
_, tb = self.get_boundaries_intersections(p_u, p_best - p_u,
trust_radius)
p_boundary = p_u + tb * (p_best - p_u)
hits_boundary = True
return p_boundary, hits_boundary
| 4,449 | 34.6 | 81 |
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|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/setup.py
|
from __future__ import division, print_function, absolute_import
from os.path import join
from scipy._build_utils import numpy_nodepr_api
def configuration(parent_package='',top_path=None):
from numpy.distutils.misc_util import Configuration
from numpy.distutils.system_info import get_info
config = Configuration('optimize',parent_package, top_path)
minpack_src = [join('minpack','*f')]
config.add_library('minpack',sources=minpack_src)
config.add_extension('_minpack',
sources=['_minpackmodule.c'],
libraries=['minpack'],
depends=(["minpack.h","__minpack.h"]
+ minpack_src),
**numpy_nodepr_api)
rootfind_src = [join('Zeros','*.c')]
rootfind_hdr = [join('Zeros','zeros.h')]
config.add_library('rootfind',
sources=rootfind_src,
headers=rootfind_hdr,
**numpy_nodepr_api)
config.add_extension('_zeros',
sources=['zeros.c'],
libraries=['rootfind'],
depends=(rootfind_src + rootfind_hdr),
**numpy_nodepr_api)
lapack = get_info('lapack_opt')
if 'define_macros' in numpy_nodepr_api:
if ('define_macros' in lapack) and (lapack['define_macros'] is not None):
lapack['define_macros'] = (lapack['define_macros'] +
numpy_nodepr_api['define_macros'])
else:
lapack['define_macros'] = numpy_nodepr_api['define_macros']
sources = ['lbfgsb.pyf', 'lbfgsb.f', 'linpack.f', 'timer.f']
config.add_extension('_lbfgsb',
sources=[join('lbfgsb',x) for x in sources],
**lapack)
sources = ['moduleTNC.c','tnc.c']
config.add_extension('moduleTNC',
sources=[join('tnc',x) for x in sources],
depends=[join('tnc','tnc.h')],
**numpy_nodepr_api)
config.add_extension('_cobyla',
sources=[join('cobyla',x) for x in ['cobyla.pyf',
'cobyla2.f',
'trstlp.f']],
**numpy_nodepr_api)
sources = ['minpack2.pyf', 'dcsrch.f', 'dcstep.f']
config.add_extension('minpack2',
sources=[join('minpack2',x) for x in sources],
**numpy_nodepr_api)
sources = ['slsqp.pyf', 'slsqp_optmz.f']
config.add_extension('_slsqp', sources=[join('slsqp', x) for x in sources],
**numpy_nodepr_api)
config.add_extension('_nnls', sources=[join('nnls', x)
for x in ["nnls.f","nnls.pyf"]],
**numpy_nodepr_api)
config.add_extension('_group_columns', sources=['_group_columns.c'],)
config.add_subpackage('_lsq')
config.add_subpackage('_trlib')
config.add_subpackage('_trustregion_constr')
config.add_data_dir('tests')
# Add license files
config.add_data_files('lbfgsb/README')
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())
| 3,405 | 36.844444 | 81 |
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|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_trustregion_exact.py
|
"""Nearly exact trust-region optimization subproblem."""
from __future__ import division, print_function, absolute_import
import numpy as np
from scipy.linalg import (norm, get_lapack_funcs, solve_triangular,
cho_solve)
from ._trustregion import (_minimize_trust_region, BaseQuadraticSubproblem)
__all__ = ['_minimize_trustregion_exact',
'estimate_smallest_singular_value',
'singular_leading_submatrix',
'IterativeSubproblem']
def _minimize_trustregion_exact(fun, x0, args=(), jac=None, hess=None,
**trust_region_options):
"""
Minimization of scalar function of one or more variables using
a nearly exact trust-region algorithm.
Options
-------
initial_tr_radius : float
Initial trust-region radius.
max_tr_radius : float
Maximum value of the trust-region radius. No steps that are longer
than this value will be proposed.
eta : float
Trust region related acceptance stringency for proposed steps.
gtol : float
Gradient norm must be less than ``gtol`` before successful
termination.
"""
if jac is None:
raise ValueError('Jacobian is required for trust region '
'exact minimization.')
if hess is None:
raise ValueError('Hessian matrix is required for trust region '
'exact minimization.')
return _minimize_trust_region(fun, x0, args=args, jac=jac, hess=hess,
subproblem=IterativeSubproblem,
**trust_region_options)
def estimate_smallest_singular_value(U):
"""Given upper triangular matrix ``U`` estimate the smallest singular
value and the correspondent right singular vector in O(n**2) operations.
Parameters
----------
U : ndarray
Square upper triangular matrix.
Returns
-------
s_min : float
Estimated smallest singular value of the provided matrix.
z_min : ndarray
Estimatied right singular vector.
Notes
-----
The procedure is based on [1]_ and is done in two steps. First it finds
a vector ``e`` with components selected from {+1, -1} such that the
solution ``w`` from the system ``U.T w = e`` is as large as possible.
Next it estimate ``U v = w``. The smallest singular value is close
to ``norm(w)/norm(v)`` and the right singular vector is close
to ``v/norm(v)``.
The estimation will be better more ill-conditioned is the matrix.
References
----------
.. [1] Cline, A. K., Moler, C. B., Stewart, G. W., Wilkinson, J. H.
An estimate for the condition number of a matrix. 1979.
SIAM Journal on Numerical Analysis, 16(2), 368-375.
"""
U = np.atleast_2d(U)
m, n = U.shape
if m != n:
raise ValueError("A square triangular matrix should be provided.")
# A vector `e` with components selected from {+1, -1}
# is selected so that the solution `w` to the system
# `U.T w = e` is as large as possible. Implementation
# based on algorithm 3.5.1, p. 142, from reference [2]
# adapted for lower triangular matrix.
p = np.zeros(n)
w = np.empty(n)
# Implemented according to: Golub, G. H., Van Loan, C. F. (2013).
# "Matrix computations". Forth Edition. JHU press. pp. 140-142.
for k in range(n):
wp = (1-p[k]) / U.T[k, k]
wm = (-1-p[k]) / U.T[k, k]
pp = p[k+1:] + U.T[k+1:, k]*wp
pm = p[k+1:] + U.T[k+1:, k]*wm
if abs(wp) + norm(pp, 1) >= abs(wm) + norm(pm, 1):
w[k] = wp
p[k+1:] = pp
else:
w[k] = wm
p[k+1:] = pm
# The system `U v = w` is solved using backward substitution.
v = solve_triangular(U, w)
v_norm = norm(v)
w_norm = norm(w)
# Smallest singular value
s_min = w_norm / v_norm
# Associated vector
z_min = v / v_norm
return s_min, z_min
def gershgorin_bounds(H):
"""
Given a square matrix ``H`` compute upper
and lower bounds for its eigenvalues (Gregoshgorin Bounds).
Defined ref. [1].
References
----------
.. [1] Conn, A. R., Gould, N. I., & Toint, P. L.
Trust region methods. 2000. Siam. pp. 19.
"""
H_diag = np.diag(H)
H_diag_abs = np.abs(H_diag)
H_row_sums = np.sum(np.abs(H), axis=1)
lb = np.min(H_diag + H_diag_abs - H_row_sums)
ub = np.max(H_diag - H_diag_abs + H_row_sums)
return lb, ub
def singular_leading_submatrix(A, U, k):
"""
Compute term that makes the leading ``k`` by ``k``
submatrix from ``A`` singular.
Parameters
----------
A : ndarray
Symmetric matrix that is not positive definite.
U : ndarray
Upper triangular matrix resulting of an incomplete
Cholesky decomposition of matrix ``A``.
k : int
Positive integer such that the leading k by k submatrix from
`A` is the first non-positive definite leading submatrix.
Returns
-------
delta : float
Amount that should be added to the element (k, k) of the
leading k by k submatrix of ``A`` to make it singular.
v : ndarray
A vector such that ``v.T B v = 0``. Where B is the matrix A after
``delta`` is added to its element (k, k).
"""
# Compute delta
delta = np.sum(U[:k-1, k-1]**2) - A[k-1, k-1]
n = len(A)
# Inicialize v
v = np.zeros(n)
v[k-1] = 1
# Compute the remaining values of v by solving a triangular system.
if k != 1:
v[:k-1] = solve_triangular(U[:k-1, :k-1], -U[:k-1, k-1])
return delta, v
class IterativeSubproblem(BaseQuadraticSubproblem):
"""Quadratic subproblem solved by nearly exact iterative method.
Notes
-----
This subproblem solver was based on [1]_, [2]_ and [3]_,
which implement similar algorithms. The algorithm is basically
that of [1]_ but ideas from [2]_ and [3]_ were also used.
References
----------
.. [1] A.R. Conn, N.I. Gould, and P.L. Toint, "Trust region methods",
Siam, pp. 169-200, 2000.
.. [2] J. Nocedal and S. Wright, "Numerical optimization",
Springer Science & Business Media. pp. 83-91, 2006.
.. [3] J.J. More and D.C. Sorensen, "Computing a trust region step",
SIAM Journal on Scientific and Statistical Computing, vol. 4(3),
pp. 553-572, 1983.
"""
# UPDATE_COEFF appears in reference [1]_
# in formula 7.3.14 (p. 190) named as "theta".
# As recommended there it value is fixed in 0.01.
UPDATE_COEFF = 0.01
EPS = np.finfo(float).eps
def __init__(self, x, fun, jac, hess, hessp=None,
k_easy=0.1, k_hard=0.2):
super(IterativeSubproblem, self).__init__(x, fun, jac, hess)
# When the trust-region shrinks in two consecutive
# calculations (``tr_radius < previous_tr_radius``)
# the lower bound ``lambda_lb`` may be reused,
# facilitating the convergence. To indicate no
# previous value is known at first ``previous_tr_radius``
# is set to -1 and ``lambda_lb`` to None.
self.previous_tr_radius = -1
self.lambda_lb = None
self.niter = 0
# ``k_easy`` and ``k_hard`` are parameters used
# to determine the stop criteria to the iterative
# subproblem solver. Take a look at pp. 194-197
# from reference _[1] for a more detailed description.
self.k_easy = k_easy
self.k_hard = k_hard
# Get Lapack function for cholesky decomposition.
# The implemented Scipy wrapper does not return
# the incomplete factorization needed by the method.
self.cholesky, = get_lapack_funcs(('potrf',), (self.hess,))
# Get info about Hessian
self.dimension = len(self.hess)
self.hess_gershgorin_lb,\
self.hess_gershgorin_ub = gershgorin_bounds(self.hess)
self.hess_inf = norm(self.hess, np.Inf)
self.hess_fro = norm(self.hess, 'fro')
# A constant such that for vectors smaler than that
# backward substituition is not reliable. It was stabilished
# based on Golub, G. H., Van Loan, C. F. (2013).
# "Matrix computations". Forth Edition. JHU press., p.165.
self.CLOSE_TO_ZERO = self.dimension * self.EPS * self.hess_inf
def _initial_values(self, tr_radius):
"""Given a trust radius, return a good initial guess for
the damping factor, the lower bound and the upper bound.
The values were chosen accordingly to the guidelines on
section 7.3.8 (p. 192) from [1]_.
"""
# Upper bound for the damping factor
lambda_ub = max(0, self.jac_mag/tr_radius + min(-self.hess_gershgorin_lb,
self.hess_fro,
self.hess_inf))
# Lower bound for the damping factor
lambda_lb = max(0, -min(self.hess.diagonal()),
self.jac_mag/tr_radius - min(self.hess_gershgorin_ub,
self.hess_fro,
self.hess_inf))
# Improve bounds with previous info
if tr_radius < self.previous_tr_radius:
lambda_lb = max(self.lambda_lb, lambda_lb)
# Initial guess for the damping factor
if lambda_lb == 0:
lambda_initial = 0
else:
lambda_initial = max(np.sqrt(lambda_lb * lambda_ub),
lambda_lb + self.UPDATE_COEFF*(lambda_ub-lambda_lb))
return lambda_initial, lambda_lb, lambda_ub
def solve(self, tr_radius):
"""Solve quadratic subproblem"""
lambda_current, lambda_lb, lambda_ub = self._initial_values(tr_radius)
n = self.dimension
hits_boundary = True
already_factorized = False
self.niter = 0
while True:
# Compute Cholesky factorization
if already_factorized:
already_factorized = False
else:
H = self.hess+lambda_current*np.eye(n)
U, info = self.cholesky(H, lower=False,
overwrite_a=False,
clean=True)
self.niter += 1
# Check if factorization succeeded
if info == 0 and self.jac_mag > self.CLOSE_TO_ZERO:
# Successful factorization
# Solve `U.T U p = s`
p = cho_solve((U, False), -self.jac)
p_norm = norm(p)
# Check for interior convergence
if p_norm <= tr_radius and lambda_current == 0:
hits_boundary = False
break
# Solve `U.T w = p`
w = solve_triangular(U, p, trans='T')
w_norm = norm(w)
# Compute Newton step accordingly to
# formula (4.44) p.87 from ref [2]_.
delta_lambda = (p_norm/w_norm)**2 * (p_norm-tr_radius)/tr_radius
lambda_new = lambda_current + delta_lambda
if p_norm < tr_radius: # Inside boundary
s_min, z_min = estimate_smallest_singular_value(U)
ta, tb = self.get_boundaries_intersections(p, z_min,
tr_radius)
# Choose `step_len` with the smallest magnitude.
# The reason for this choice is explained at
# ref [3]_, p. 6 (Immediately before the formula
# for `tau`).
step_len = min([ta, tb], key=abs)
# Compute the quadratic term (p.T*H*p)
quadratic_term = np.dot(p, np.dot(H, p))
# Check stop criteria
relative_error = (step_len**2 * s_min**2) / (quadratic_term + lambda_current*tr_radius**2)
if relative_error <= self.k_hard:
p += step_len * z_min
break
# Update uncertanty bounds
lambda_ub = lambda_current
lambda_lb = max(lambda_lb, lambda_current - s_min**2)
# Compute Cholesky factorization
H = self.hess + lambda_new*np.eye(n)
c, info = self.cholesky(H, lower=False,
overwrite_a=False,
clean=True)
# Check if the factorization have succeeded
#
if info == 0: # Successful factorization
# Update damping factor
lambda_current = lambda_new
already_factorized = True
else: # Unsuccessful factorization
# Update uncertanty bounds
lambda_lb = max(lambda_lb, lambda_new)
# Update damping factor
lambda_current = max(np.sqrt(lambda_lb * lambda_ub),
lambda_lb + self.UPDATE_COEFF*(lambda_ub-lambda_lb))
else: # Outside boundary
# Check stop criteria
relative_error = abs(p_norm - tr_radius) / tr_radius
if relative_error <= self.k_easy:
break
# Update uncertanty bounds
lambda_lb = lambda_current
# Update damping factor
lambda_current = lambda_new
elif info == 0 and self.jac_mag <= self.CLOSE_TO_ZERO:
# jac_mag very close to zero
# Check for interior convergence
if lambda_current == 0:
p = np.zeros(n)
hits_boundary = False
break
s_min, z_min = estimate_smallest_singular_value(U)
step_len = tr_radius
# Check stop criteria
if step_len**2 * s_min**2 <= self.k_hard * lambda_current * tr_radius**2:
p = step_len * z_min
break
# Update uncertanty bounds
lambda_ub = lambda_current
lambda_lb = max(lambda_lb, lambda_current - s_min**2)
# Update damping factor
lambda_current = max(np.sqrt(lambda_lb * lambda_ub),
lambda_lb + self.UPDATE_COEFF*(lambda_ub-lambda_lb))
else: # Unsuccessful factorization
# Compute auxiliary terms
delta, v = singular_leading_submatrix(H, U, info)
v_norm = norm(v)
# Update uncertanty interval
lambda_lb = max(lambda_lb, lambda_current + delta/v_norm**2)
# Update damping factor
lambda_current = max(np.sqrt(lambda_lb * lambda_ub),
lambda_lb + self.UPDATE_COEFF*(lambda_ub-lambda_lb))
self.lambda_lb = lambda_lb
self.lambda_current = lambda_current
self.previous_tr_radius = tr_radius
return p, hits_boundary
| 15,492 | 34.7806 | 110 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_tstutils.py
|
''' Parameters used in test and benchmark methods '''
from __future__ import division, print_function, absolute_import
from random import random
from scipy.optimize import zeros as cc
def f1(x):
return x*(x-1.)
def f2(x):
return x**2 - 1
def f3(x):
return x*(x-1.)*(x-2.)*(x-3.)
def f4(x):
if x > 1:
return 1.0 + .1*x
if x < 1:
return -1.0 + .1*x
return 0
def f5(x):
if x != 1:
return 1.0/(1. - x)
return 0
def f6(x):
if x > 1:
return random()
elif x < 1:
return -random()
else:
return 0
description = """
f2 is a symmetric parabola, x**2 - 1
f3 is a quartic polynomial with large hump in interval
f4 is step function with a discontinuity at 1
f5 is a hyperbola with vertical asymptote at 1
f6 has random values positive to left of 1, negative to right
of course these are not real problems. They just test how the
'good' solvers behave in bad circumstances where bisection is
really the best. A good solver should not be much worse than
bisection in such circumstance, while being faster for smooth
monotone sorts of functions.
"""
methods = [cc.bisect,cc.ridder,cc.brenth,cc.brentq]
mstrings = ['cc.bisect','cc.ridder','cc.brenth','cc.brentq']
functions = [f2,f3,f4,f5,f6]
fstrings = ['f2','f3','f4','f5','f6']
| 1,323 | 20.354839 | 64 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_trustregion_ncg.py
|
"""Newton-CG trust-region optimization."""
from __future__ import division, print_function, absolute_import
import math
import numpy as np
import scipy.linalg
from ._trustregion import (_minimize_trust_region, BaseQuadraticSubproblem)
__all__ = []
def _minimize_trust_ncg(fun, x0, args=(), jac=None, hess=None, hessp=None,
**trust_region_options):
"""
Minimization of scalar function of one or more variables using
the Newton conjugate gradient trust-region algorithm.
Options
-------
initial_trust_radius : float
Initial trust-region radius.
max_trust_radius : float
Maximum value of the trust-region radius. No steps that are longer
than this value will be proposed.
eta : float
Trust region related acceptance stringency for proposed steps.
gtol : float
Gradient norm must be less than `gtol` before successful
termination.
"""
if jac is None:
raise ValueError('Jacobian is required for Newton-CG trust-region '
'minimization')
if hess is None and hessp is None:
raise ValueError('Either the Hessian or the Hessian-vector product '
'is required for Newton-CG trust-region minimization')
return _minimize_trust_region(fun, x0, args=args, jac=jac, hess=hess,
hessp=hessp, subproblem=CGSteihaugSubproblem,
**trust_region_options)
class CGSteihaugSubproblem(BaseQuadraticSubproblem):
"""Quadratic subproblem solved by a conjugate gradient method"""
def solve(self, trust_radius):
"""
Solve the subproblem using a conjugate gradient method.
Parameters
----------
trust_radius : float
We are allowed to wander only this far away from the origin.
Returns
-------
p : ndarray
The proposed step.
hits_boundary : bool
True if the proposed step is on the boundary of the trust region.
Notes
-----
This is algorithm (7.2) of Nocedal and Wright 2nd edition.
Only the function that computes the Hessian-vector product is required.
The Hessian itself is not required, and the Hessian does
not need to be positive semidefinite.
"""
# get the norm of jacobian and define the origin
p_origin = np.zeros_like(self.jac)
# define a default tolerance
tolerance = min(0.5, math.sqrt(self.jac_mag)) * self.jac_mag
# Stop the method if the search direction
# is a direction of nonpositive curvature.
if self.jac_mag < tolerance:
hits_boundary = False
return p_origin, hits_boundary
# init the state for the first iteration
z = p_origin
r = self.jac
d = -r
# Search for the min of the approximation of the objective function.
while True:
# do an iteration
Bd = self.hessp(d)
dBd = np.dot(d, Bd)
if dBd <= 0:
# Look at the two boundary points.
# Find both values of t to get the boundary points such that
# ||z + t d|| == trust_radius
# and then choose the one with the predicted min value.
ta, tb = self.get_boundaries_intersections(z, d, trust_radius)
pa = z + ta * d
pb = z + tb * d
if self(pa) < self(pb):
p_boundary = pa
else:
p_boundary = pb
hits_boundary = True
return p_boundary, hits_boundary
r_squared = np.dot(r, r)
alpha = r_squared / dBd
z_next = z + alpha * d
if scipy.linalg.norm(z_next) >= trust_radius:
# Find t >= 0 to get the boundary point such that
# ||z + t d|| == trust_radius
ta, tb = self.get_boundaries_intersections(z, d, trust_radius)
p_boundary = z + tb * d
hits_boundary = True
return p_boundary, hits_boundary
r_next = r + alpha * Bd
r_next_squared = np.dot(r_next, r_next)
if math.sqrt(r_next_squared) < tolerance:
hits_boundary = False
return z_next, hits_boundary
beta_next = r_next_squared / r_squared
d_next = -r_next + beta_next * d
# update the state for the next iteration
z = z_next
r = r_next
d = d_next
| 4,646 | 35.023256 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_root.py
|
"""
Unified interfaces to root finding algorithms.
Functions
---------
- root : find a root of a vector function.
"""
from __future__ import division, print_function, absolute_import
__all__ = ['root']
import numpy as np
from scipy._lib.six import callable
from warnings import warn
from .optimize import MemoizeJac, OptimizeResult, _check_unknown_options
from .minpack import _root_hybr, leastsq
from ._spectral import _root_df_sane
from . import nonlin
def root(fun, x0, args=(), method='hybr', jac=None, tol=None, callback=None,
options=None):
"""
Find a root of a vector function.
Parameters
----------
fun : callable
A vector function to find a root of.
x0 : ndarray
Initial guess.
args : tuple, optional
Extra arguments passed to the objective function and its Jacobian.
method : str, optional
Type of solver. Should be one of
- 'hybr' :ref:`(see here) <optimize.root-hybr>`
- 'lm' :ref:`(see here) <optimize.root-lm>`
- 'broyden1' :ref:`(see here) <optimize.root-broyden1>`
- 'broyden2' :ref:`(see here) <optimize.root-broyden2>`
- 'anderson' :ref:`(see here) <optimize.root-anderson>`
- 'linearmixing' :ref:`(see here) <optimize.root-linearmixing>`
- 'diagbroyden' :ref:`(see here) <optimize.root-diagbroyden>`
- 'excitingmixing' :ref:`(see here) <optimize.root-excitingmixing>`
- 'krylov' :ref:`(see here) <optimize.root-krylov>`
- 'df-sane' :ref:`(see here) <optimize.root-dfsane>`
jac : bool or callable, optional
If `jac` is a Boolean and is True, `fun` is assumed to return the
value of Jacobian along with the objective function. If False, the
Jacobian will be estimated numerically.
`jac` can also be a callable returning the Jacobian of `fun`. In
this case, it must accept the same arguments as `fun`.
tol : float, optional
Tolerance for termination. For detailed control, use solver-specific
options.
callback : function, optional
Optional callback function. It is called on every iteration as
``callback(x, f)`` where `x` is the current solution and `f`
the corresponding residual. For all methods but 'hybr' and 'lm'.
options : dict, optional
A dictionary of solver options. E.g. `xtol` or `maxiter`, see
:obj:`show_options()` for details.
Returns
-------
sol : OptimizeResult
The solution represented as a ``OptimizeResult`` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the algorithm exited successfully and
``message`` which describes the cause of the termination. See
`OptimizeResult` for a description of other attributes.
See also
--------
show_options : Additional options accepted by the solvers
Notes
-----
This section describes the available solvers that can be selected by the
'method' parameter. The default method is *hybr*.
Method *hybr* uses a modification of the Powell hybrid method as
implemented in MINPACK [1]_.
Method *lm* solves the system of nonlinear equations in a least squares
sense using a modification of the Levenberg-Marquardt algorithm as
implemented in MINPACK [1]_.
Method *df-sane* is a derivative-free spectral method. [3]_
Methods *broyden1*, *broyden2*, *anderson*, *linearmixing*,
*diagbroyden*, *excitingmixing*, *krylov* are inexact Newton methods,
with backtracking or full line searches [2]_. Each method corresponds
to a particular Jacobian approximations. See `nonlin` for details.
- Method *broyden1* uses Broyden's first Jacobian approximation, it is
known as Broyden's good method.
- Method *broyden2* uses Broyden's second Jacobian approximation, it
is known as Broyden's bad method.
- Method *anderson* uses (extended) Anderson mixing.
- Method *Krylov* uses Krylov approximation for inverse Jacobian. It
is suitable for large-scale problem.
- Method *diagbroyden* uses diagonal Broyden Jacobian approximation.
- Method *linearmixing* uses a scalar Jacobian approximation.
- Method *excitingmixing* uses a tuned diagonal Jacobian
approximation.
.. warning::
The algorithms implemented for methods *diagbroyden*,
*linearmixing* and *excitingmixing* may be useful for specific
problems, but whether they will work may depend strongly on the
problem.
.. versionadded:: 0.11.0
References
----------
.. [1] More, Jorge J., Burton S. Garbow, and Kenneth E. Hillstrom.
1980. User Guide for MINPACK-1.
.. [2] C. T. Kelley. 1995. Iterative Methods for Linear and Nonlinear
Equations. Society for Industrial and Applied Mathematics.
<http://www.siam.org/books/kelley/fr16/index.php>
.. [3] W. La Cruz, J.M. Martinez, M. Raydan. Math. Comp. 75, 1429 (2006).
Examples
--------
The following functions define a system of nonlinear equations and its
jacobian.
>>> def fun(x):
... return [x[0] + 0.5 * (x[0] - x[1])**3 - 1.0,
... 0.5 * (x[1] - x[0])**3 + x[1]]
>>> def jac(x):
... return np.array([[1 + 1.5 * (x[0] - x[1])**2,
... -1.5 * (x[0] - x[1])**2],
... [-1.5 * (x[1] - x[0])**2,
... 1 + 1.5 * (x[1] - x[0])**2]])
A solution can be obtained as follows.
>>> from scipy import optimize
>>> sol = optimize.root(fun, [0, 0], jac=jac, method='hybr')
>>> sol.x
array([ 0.8411639, 0.1588361])
"""
if not isinstance(args, tuple):
args = (args,)
meth = method.lower()
if options is None:
options = {}
if callback is not None and meth in ('hybr', 'lm'):
warn('Method %s does not accept callback.' % method,
RuntimeWarning)
# fun also returns the jacobian
if not callable(jac) and meth in ('hybr', 'lm'):
if bool(jac):
fun = MemoizeJac(fun)
jac = fun.derivative
else:
jac = None
# set default tolerances
if tol is not None:
options = dict(options)
if meth in ('hybr', 'lm'):
options.setdefault('xtol', tol)
elif meth in ('df-sane',):
options.setdefault('ftol', tol)
elif meth in ('broyden1', 'broyden2', 'anderson', 'linearmixing',
'diagbroyden', 'excitingmixing', 'krylov'):
options.setdefault('xtol', tol)
options.setdefault('xatol', np.inf)
options.setdefault('ftol', np.inf)
options.setdefault('fatol', np.inf)
if meth == 'hybr':
sol = _root_hybr(fun, x0, args=args, jac=jac, **options)
elif meth == 'lm':
sol = _root_leastsq(fun, x0, args=args, jac=jac, **options)
elif meth == 'df-sane':
_warn_jac_unused(jac, method)
sol = _root_df_sane(fun, x0, args=args, callback=callback,
**options)
elif meth in ('broyden1', 'broyden2', 'anderson', 'linearmixing',
'diagbroyden', 'excitingmixing', 'krylov'):
_warn_jac_unused(jac, method)
sol = _root_nonlin_solve(fun, x0, args=args, jac=jac,
_method=meth, _callback=callback,
**options)
else:
raise ValueError('Unknown solver %s' % method)
return sol
def _warn_jac_unused(jac, method):
if jac is not None:
warn('Method %s does not use the jacobian (jac).' % (method,),
RuntimeWarning)
def _root_leastsq(func, x0, args=(), jac=None,
col_deriv=0, xtol=1.49012e-08, ftol=1.49012e-08,
gtol=0.0, maxiter=0, eps=0.0, factor=100, diag=None,
**unknown_options):
"""
Solve for least squares with Levenberg-Marquardt
Options
-------
col_deriv : bool
non-zero to specify that the Jacobian function computes derivatives
down the columns (faster, because there is no transpose operation).
ftol : float
Relative error desired in the sum of squares.
xtol : float
Relative error desired in the approximate solution.
gtol : float
Orthogonality desired between the function vector and the columns
of the Jacobian.
maxiter : int
The maximum number of calls to the function. If zero, then
100*(N+1) is the maximum where N is the number of elements in x0.
epsfcn : float
A suitable step length for the forward-difference approximation of
the Jacobian (for Dfun=None). If epsfcn is less than the machine
precision, it is assumed that the relative errors in the functions
are of the order of the machine precision.
factor : float
A parameter determining the initial step bound
(``factor * || diag * x||``). Should be in interval ``(0.1, 100)``.
diag : sequence
N positive entries that serve as a scale factors for the variables.
"""
_check_unknown_options(unknown_options)
x, cov_x, info, msg, ier = leastsq(func, x0, args=args, Dfun=jac,
full_output=True,
col_deriv=col_deriv, xtol=xtol,
ftol=ftol, gtol=gtol,
maxfev=maxiter, epsfcn=eps,
factor=factor, diag=diag)
sol = OptimizeResult(x=x, message=msg, status=ier,
success=ier in (1, 2, 3, 4), cov_x=cov_x,
fun=info.pop('fvec'))
sol.update(info)
return sol
def _root_nonlin_solve(func, x0, args=(), jac=None,
_callback=None, _method=None,
nit=None, disp=False, maxiter=None,
ftol=None, fatol=None, xtol=None, xatol=None,
tol_norm=None, line_search='armijo', jac_options=None,
**unknown_options):
_check_unknown_options(unknown_options)
f_tol = fatol
f_rtol = ftol
x_tol = xatol
x_rtol = xtol
verbose = disp
if jac_options is None:
jac_options = dict()
jacobian = {'broyden1': nonlin.BroydenFirst,
'broyden2': nonlin.BroydenSecond,
'anderson': nonlin.Anderson,
'linearmixing': nonlin.LinearMixing,
'diagbroyden': nonlin.DiagBroyden,
'excitingmixing': nonlin.ExcitingMixing,
'krylov': nonlin.KrylovJacobian
}[_method]
if args:
if jac:
def f(x):
return func(x, *args)[0]
else:
def f(x):
return func(x, *args)
else:
f = func
x, info = nonlin.nonlin_solve(f, x0, jacobian=jacobian(**jac_options),
iter=nit, verbose=verbose,
maxiter=maxiter, f_tol=f_tol,
f_rtol=f_rtol, x_tol=x_tol,
x_rtol=x_rtol, tol_norm=tol_norm,
line_search=line_search,
callback=_callback, full_output=True,
raise_exception=False)
sol = OptimizeResult(x=x)
sol.update(info)
return sol
def _root_broyden1_doc():
"""
Options
-------
nit : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
disp : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, `NoConvergence` is raised.
ftol : float, optional
Relative tolerance for the residual. If omitted, not used.
fatol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
xtol : float, optional
Relative minimum step size. If omitted, not used.
xatol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in
the direction given by the Jacobian approximation. Defaults to
'armijo'.
jac_options : dict, optional
Options for the respective Jacobian approximation.
alpha : float, optional
Initial guess for the Jacobian is (-1/alpha).
reduction_method : str or tuple, optional
Method used in ensuring that the rank of the Broyden
matrix stays low. Can either be a string giving the
name of the method, or a tuple of the form ``(method,
param1, param2, ...)`` that gives the name of the
method and values for additional parameters.
Methods available:
- ``restart``: drop all matrix columns. Has no
extra parameters.
- ``simple``: drop oldest matrix column. Has no
extra parameters.
- ``svd``: keep only the most significant SVD
components.
Extra parameters:
- ``to_retain``: number of SVD components to
retain when rank reduction is done.
Default is ``max_rank - 2``.
max_rank : int, optional
Maximum rank for the Broyden matrix.
Default is infinity (ie., no rank reduction).
"""
pass
def _root_broyden2_doc():
"""
Options
-------
nit : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
disp : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, `NoConvergence` is raised.
ftol : float, optional
Relative tolerance for the residual. If omitted, not used.
fatol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
xtol : float, optional
Relative minimum step size. If omitted, not used.
xatol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in
the direction given by the Jacobian approximation. Defaults to
'armijo'.
jac_options : dict, optional
Options for the respective Jacobian approximation.
alpha : float, optional
Initial guess for the Jacobian is (-1/alpha).
reduction_method : str or tuple, optional
Method used in ensuring that the rank of the Broyden
matrix stays low. Can either be a string giving the
name of the method, or a tuple of the form ``(method,
param1, param2, ...)`` that gives the name of the
method and values for additional parameters.
Methods available:
- ``restart``: drop all matrix columns. Has no
extra parameters.
- ``simple``: drop oldest matrix column. Has no
extra parameters.
- ``svd``: keep only the most significant SVD
components.
Extra parameters:
- ``to_retain``: number of SVD components to
retain when rank reduction is done.
Default is ``max_rank - 2``.
max_rank : int, optional
Maximum rank for the Broyden matrix.
Default is infinity (ie., no rank reduction).
"""
pass
def _root_anderson_doc():
"""
Options
-------
nit : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
disp : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, `NoConvergence` is raised.
ftol : float, optional
Relative tolerance for the residual. If omitted, not used.
fatol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
xtol : float, optional
Relative minimum step size. If omitted, not used.
xatol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in
the direction given by the Jacobian approximation. Defaults to
'armijo'.
jac_options : dict, optional
Options for the respective Jacobian approximation.
alpha : float, optional
Initial guess for the Jacobian is (-1/alpha).
M : float, optional
Number of previous vectors to retain. Defaults to 5.
w0 : float, optional
Regularization parameter for numerical stability.
Compared to unity, good values of the order of 0.01.
"""
pass
def _root_linearmixing_doc():
"""
Options
-------
nit : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
disp : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, ``NoConvergence`` is raised.
ftol : float, optional
Relative tolerance for the residual. If omitted, not used.
fatol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
xtol : float, optional
Relative minimum step size. If omitted, not used.
xatol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in
the direction given by the Jacobian approximation. Defaults to
'armijo'.
jac_options : dict, optional
Options for the respective Jacobian approximation.
alpha : float, optional
initial guess for the jacobian is (-1/alpha).
"""
pass
def _root_diagbroyden_doc():
"""
Options
-------
nit : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
disp : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, `NoConvergence` is raised.
ftol : float, optional
Relative tolerance for the residual. If omitted, not used.
fatol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
xtol : float, optional
Relative minimum step size. If omitted, not used.
xatol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in
the direction given by the Jacobian approximation. Defaults to
'armijo'.
jac_options : dict, optional
Options for the respective Jacobian approximation.
alpha : float, optional
initial guess for the jacobian is (-1/alpha).
"""
pass
def _root_excitingmixing_doc():
"""
Options
-------
nit : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
disp : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, `NoConvergence` is raised.
ftol : float, optional
Relative tolerance for the residual. If omitted, not used.
fatol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
xtol : float, optional
Relative minimum step size. If omitted, not used.
xatol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in
the direction given by the Jacobian approximation. Defaults to
'armijo'.
jac_options : dict, optional
Options for the respective Jacobian approximation.
alpha : float, optional
Initial Jacobian approximation is (-1/alpha).
alphamax : float, optional
The entries of the diagonal Jacobian are kept in the range
``[alpha, alphamax]``.
"""
pass
def _root_krylov_doc():
"""
Options
-------
nit : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
disp : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, `NoConvergence` is raised.
ftol : float, optional
Relative tolerance for the residual. If omitted, not used.
fatol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
xtol : float, optional
Relative minimum step size. If omitted, not used.
xatol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in
the direction given by the Jacobian approximation. Defaults to
'armijo'.
jac_options : dict, optional
Options for the respective Jacobian approximation.
rdiff : float, optional
Relative step size to use in numerical differentiation.
method : {'lgmres', 'gmres', 'bicgstab', 'cgs', 'minres'} or function
Krylov method to use to approximate the Jacobian.
Can be a string, or a function implementing the same
interface as the iterative solvers in
`scipy.sparse.linalg`.
The default is `scipy.sparse.linalg.lgmres`.
inner_M : LinearOperator or InverseJacobian
Preconditioner for the inner Krylov iteration.
Note that you can use also inverse Jacobians as (adaptive)
preconditioners. For example,
>>> jac = BroydenFirst()
>>> kjac = KrylovJacobian(inner_M=jac.inverse).
If the preconditioner has a method named 'update', it will
be called as ``update(x, f)`` after each nonlinear step,
with ``x`` giving the current point, and ``f`` the current
function value.
inner_tol, inner_maxiter, ...
Parameters to pass on to the "inner" Krylov solver.
See `scipy.sparse.linalg.gmres` for details.
outer_k : int, optional
Size of the subspace kept across LGMRES nonlinear
iterations.
See `scipy.sparse.linalg.lgmres` for details.
"""
pass
| 26,020 | 39.594384 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_linprog.py
|
"""
A top-level linear programming interface. Currently this interface only
solves linear programming problems via the Simplex Method.
.. versionadded:: 0.15.0
Functions
---------
.. autosummary::
:toctree: generated/
linprog
linprog_verbose_callback
linprog_terse_callback
"""
from __future__ import division, print_function, absolute_import
import numpy as np
from .optimize import OptimizeResult, _check_unknown_options
from ._linprog_ip import _linprog_ip
__all__ = ['linprog', 'linprog_verbose_callback', 'linprog_terse_callback']
__docformat__ = "restructuredtext en"
def linprog_verbose_callback(xk, **kwargs):
"""
A sample callback function demonstrating the linprog callback interface.
This callback produces detailed output to sys.stdout before each iteration
and after the final iteration of the simplex algorithm.
Parameters
----------
xk : array_like
The current solution vector.
**kwargs : dict
A dictionary containing the following parameters:
tableau : array_like
The current tableau of the simplex algorithm.
Its structure is defined in _solve_simplex.
phase : int
The current Phase of the simplex algorithm (1 or 2)
nit : int
The current iteration number.
pivot : tuple(int, int)
The index of the tableau selected as the next pivot,
or nan if no pivot exists
basis : array(int)
A list of the current basic variables.
Each element contains the name of a basic variable and its value.
complete : bool
True if the simplex algorithm has completed
(and this is the final call to callback), otherwise False.
"""
tableau = kwargs["tableau"]
nit = kwargs["nit"]
pivrow, pivcol = kwargs["pivot"]
phase = kwargs["phase"]
basis = kwargs["basis"]
complete = kwargs["complete"]
saved_printoptions = np.get_printoptions()
np.set_printoptions(linewidth=500,
formatter={'float': lambda x: "{0: 12.4f}".format(x)})
if complete:
print("--------- Iteration Complete - Phase {0:d} -------\n".format(phase))
print("Tableau:")
elif nit == 0:
print("--------- Initial Tableau - Phase {0:d} ----------\n".format(phase))
else:
print("--------- Iteration {0:d} - Phase {1:d} --------\n".format(nit, phase))
print("Tableau:")
if nit >= 0:
print("" + str(tableau) + "\n")
if not complete:
print("Pivot Element: T[{0:.0f}, {1:.0f}]\n".format(pivrow, pivcol))
print("Basic Variables:", basis)
print()
print("Current Solution:")
print("x = ", xk)
print()
print("Current Objective Value:")
print("f = ", -tableau[-1, -1])
print()
np.set_printoptions(**saved_printoptions)
def linprog_terse_callback(xk, **kwargs):
"""
A sample callback function demonstrating the linprog callback interface.
This callback produces brief output to sys.stdout before each iteration
and after the final iteration of the simplex algorithm.
Parameters
----------
xk : array_like
The current solution vector.
**kwargs : dict
A dictionary containing the following parameters:
tableau : array_like
The current tableau of the simplex algorithm.
Its structure is defined in _solve_simplex.
vars : tuple(str, ...)
Column headers for each column in tableau.
"x[i]" for actual variables, "s[i]" for slack surplus variables,
"a[i]" for artificial variables, and "RHS" for the constraint
RHS vector.
phase : int
The current Phase of the simplex algorithm (1 or 2)
nit : int
The current iteration number.
pivot : tuple(int, int)
The index of the tableau selected as the next pivot,
or nan if no pivot exists
basics : list[tuple(int, float)]
A list of the current basic variables.
Each element contains the index of a basic variable and
its value.
complete : bool
True if the simplex algorithm has completed
(and this is the final call to callback), otherwise False.
"""
nit = kwargs["nit"]
if nit == 0:
print("Iter: X:")
print("{0: <5d} ".format(nit), end="")
print(xk)
def _pivot_col(T, tol=1.0E-12, bland=False):
"""
Given a linear programming simplex tableau, determine the column
of the variable to enter the basis.
Parameters
----------
T : 2D ndarray
The simplex tableau.
tol : float
Elements in the objective row larger than -tol will not be considered
for pivoting. Nominally this value is zero, but numerical issues
cause a tolerance about zero to be necessary.
bland : bool
If True, use Bland's rule for selection of the column (select the
first column with a negative coefficient in the objective row,
regardless of magnitude).
Returns
-------
status: bool
True if a suitable pivot column was found, otherwise False.
A return of False indicates that the linear programming simplex
algorithm is complete.
col: int
The index of the column of the pivot element.
If status is False, col will be returned as nan.
"""
ma = np.ma.masked_where(T[-1, :-1] >= -tol, T[-1, :-1], copy=False)
if ma.count() == 0:
return False, np.nan
if bland:
return True, np.where(ma.mask == False)[0][0]
return True, np.ma.where(ma == ma.min())[0][0]
def _pivot_row(T, basis, pivcol, phase, tol=1.0E-12, bland=False):
"""
Given a linear programming simplex tableau, determine the row for the
pivot operation.
Parameters
----------
T : 2D ndarray
The simplex tableau.
basis : array
A list of the current basic variables.
pivcol : int
The index of the pivot column.
phase : int
The phase of the simplex algorithm (1 or 2).
tol : float
Elements in the pivot column smaller than tol will not be considered
for pivoting. Nominally this value is zero, but numerical issues
cause a tolerance about zero to be necessary.
bland : bool
If True, use Bland's rule for selection of the row (if more than one
row can be used, choose the one with the lowest variable index).
Returns
-------
status: bool
True if a suitable pivot row was found, otherwise False. A return
of False indicates that the linear programming problem is unbounded.
row: int
The index of the row of the pivot element. If status is False, row
will be returned as nan.
"""
if phase == 1:
k = 2
else:
k = 1
ma = np.ma.masked_where(T[:-k, pivcol] <= tol, T[:-k, pivcol], copy=False)
if ma.count() == 0:
return False, np.nan
mb = np.ma.masked_where(T[:-k, pivcol] <= tol, T[:-k, -1], copy=False)
q = mb / ma
min_rows = np.ma.where(q == q.min())[0]
if bland:
return True, min_rows[np.argmin(np.take(basis, min_rows))]
return True, min_rows[0]
def _solve_simplex(T, n, basis, maxiter=1000, phase=2, callback=None,
tol=1.0E-12, nit0=0, bland=False):
"""
Solve a linear programming problem in "standard maximization form" using
the Simplex Method.
Minimize :math:`f = c^T x`
subject to
.. math::
Ax = b
x_i >= 0
b_j >= 0
Parameters
----------
T : array_like
A 2-D array representing the simplex T corresponding to the
maximization problem. It should have the form:
[[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
[A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
.
.
.
[A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
[c[0], c[1], ..., c[n_total], 0]]
for a Phase 2 problem, or the form:
[[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
[A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
.
.
.
[A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
[c[0], c[1], ..., c[n_total], 0],
[c'[0], c'[1], ..., c'[n_total], 0]]
for a Phase 1 problem (a Problem in which a basic feasible solution is
sought prior to maximizing the actual objective. T is modified in
place by _solve_simplex.
n : int
The number of true variables in the problem.
basis : array
An array of the indices of the basic variables, such that basis[i]
contains the column corresponding to the basic variable for row i.
Basis is modified in place by _solve_simplex
maxiter : int
The maximum number of iterations to perform before aborting the
optimization.
phase : int
The phase of the optimization being executed. In phase 1 a basic
feasible solution is sought and the T has an additional row
representing an alternate objective function.
callback : callable, optional
If a callback function is provided, it will be called within each
iteration of the simplex algorithm. The callback must have the
signature `callback(xk, **kwargs)` where xk is the current solution
vector and kwargs is a dictionary containing the following::
"T" : The current Simplex algorithm T
"nit" : The current iteration.
"pivot" : The pivot (row, column) used for the next iteration.
"phase" : Whether the algorithm is in Phase 1 or Phase 2.
"basis" : The indices of the columns of the basic variables.
tol : float
The tolerance which determines when a solution is "close enough" to
zero in Phase 1 to be considered a basic feasible solution or close
enough to positive to serve as an optimal solution.
nit0 : int
The initial iteration number used to keep an accurate iteration total
in a two-phase problem.
bland : bool
If True, choose pivots using Bland's rule [3]. In problems which
fail to converge due to cycling, using Bland's rule can provide
convergence at the expense of a less optimal path about the simplex.
Returns
-------
res : OptimizeResult
The optimization result represented as a ``OptimizeResult`` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. Possible
values for the ``status`` attribute are:
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
See `OptimizeResult` for a description of other attributes.
"""
nit = nit0
complete = False
if phase == 1:
m = T.shape[0]-2
elif phase == 2:
m = T.shape[0]-1
else:
raise ValueError("Argument 'phase' to _solve_simplex must be 1 or 2")
if phase == 2:
# Check if any artificial variables are still in the basis.
# If yes, check if any coefficients from this row and a column
# corresponding to one of the non-artificial variable is non-zero.
# If found, pivot at this term. If not, start phase 2.
# Do this for all artificial variables in the basis.
# Ref: "An Introduction to Linear Programming and Game Theory"
# by Paul R. Thie, Gerard E. Keough, 3rd Ed,
# Chapter 3.7 Redundant Systems (pag 102)
for pivrow in [row for row in range(basis.size)
if basis[row] > T.shape[1] - 2]:
non_zero_row = [col for col in range(T.shape[1] - 1)
if T[pivrow, col] != 0]
if len(non_zero_row) > 0:
pivcol = non_zero_row[0]
# variable represented by pivcol enters
# variable in basis[pivrow] leaves
basis[pivrow] = pivcol
pivval = T[pivrow][pivcol]
T[pivrow, :] = T[pivrow, :] / pivval
for irow in range(T.shape[0]):
if irow != pivrow:
T[irow, :] = T[irow, :] - T[pivrow, :]*T[irow, pivcol]
nit += 1
if len(basis[:m]) == 0:
solution = np.zeros(T.shape[1] - 1, dtype=np.float64)
else:
solution = np.zeros(max(T.shape[1] - 1, max(basis[:m]) + 1),
dtype=np.float64)
while not complete:
# Find the pivot column
pivcol_found, pivcol = _pivot_col(T, tol, bland)
if not pivcol_found:
pivcol = np.nan
pivrow = np.nan
status = 0
complete = True
else:
# Find the pivot row
pivrow_found, pivrow = _pivot_row(T, basis, pivcol, phase, tol, bland)
if not pivrow_found:
status = 3
complete = True
if callback is not None:
solution[:] = 0
solution[basis[:m]] = T[:m, -1]
callback(solution[:n], **{"tableau": T,
"phase": phase,
"nit": nit,
"pivot": (pivrow, pivcol),
"basis": basis,
"complete": complete and phase == 2})
if not complete:
if nit >= maxiter:
# Iteration limit exceeded
status = 1
complete = True
else:
# variable represented by pivcol enters
# variable in basis[pivrow] leaves
basis[pivrow] = pivcol
pivval = T[pivrow][pivcol]
T[pivrow, :] = T[pivrow, :] / pivval
for irow in range(T.shape[0]):
if irow != pivrow:
T[irow, :] = T[irow, :] - T[pivrow, :]*T[irow, pivcol]
nit += 1
return nit, status
def _linprog_simplex(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None,
bounds=None, maxiter=1000, disp=False, callback=None,
tol=1.0E-12, bland=False, **unknown_options):
"""
Solve the following linear programming problem via a two-phase
simplex algorithm.::
minimize: c^T * x
subject to: A_ub * x <= b_ub
A_eq * x == b_eq
Parameters
----------
c : array_like
Coefficients of the linear objective function to be minimized.
A_ub : array_like
2-D array which, when matrix-multiplied by ``x``, gives the values of
the upper-bound inequality constraints at ``x``.
b_ub : array_like
1-D array of values representing the upper-bound of each inequality
constraint (row) in ``A_ub``.
A_eq : array_like
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x``.
b_eq : array_like
1-D array of values representing the RHS of each equality constraint
(row) in ``A_eq``.
bounds : array_like
The bounds for each independent variable in the solution, which can
take one of three forms::
None : The default bounds, all variables are non-negative.
(lb, ub) : If a 2-element sequence is provided, the same
lower bound (lb) and upper bound (ub) will be applied
to all variables.
[(lb_0, ub_0), (lb_1, ub_1), ...] : If an n x 2 sequence is provided,
each variable x_i will be bounded by lb[i] and ub[i].
Infinite bounds are specified using -np.inf (negative)
or np.inf (positive).
callback : callable
If a callback function is provide, it will be called within each
iteration of the simplex algorithm. The callback must have the
signature ``callback(xk, **kwargs)`` where ``xk`` is the current s
olution vector and kwargs is a dictionary containing the following::
"tableau" : The current Simplex algorithm tableau
"nit" : The current iteration.
"pivot" : The pivot (row, column) used for the next iteration.
"phase" : Whether the algorithm is in Phase 1 or Phase 2.
"bv" : A structured array containing a string representation of each
basic variable and its current value.
Options
-------
maxiter : int
The maximum number of iterations to perform.
disp : bool
If True, print exit status message to sys.stdout
tol : float
The tolerance which determines when a solution is "close enough" to
zero in Phase 1 to be considered a basic feasible solution or close
enough to positive to serve as an optimal solution.
bland : bool
If True, use Bland's anti-cycling rule [3] to choose pivots to
prevent cycling. If False, choose pivots which should lead to a
converged solution more quickly. The latter method is subject to
cycling (non-convergence) in rare instances.
Returns
-------
A `scipy.optimize.OptimizeResult` consisting of the following fields:
x : ndarray
The independent variable vector which optimizes the linear
programming problem.
fun : float
Value of the objective function.
slack : ndarray
The values of the slack variables. Each slack variable corresponds
to an inequality constraint. If the slack is zero, then the
corresponding constraint is active.
success : bool
Returns True if the algorithm succeeded in finding an optimal
solution.
status : int
An integer representing the exit status of the optimization::
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
nit : int
The number of iterations performed.
message : str
A string descriptor of the exit status of the optimization.
Examples
--------
Consider the following problem:
Minimize: f = -1*x[0] + 4*x[1]
Subject to: -3*x[0] + 1*x[1] <= 6
1*x[0] + 2*x[1] <= 4
x[1] >= -3
where: -inf <= x[0] <= inf
This problem deviates from the standard linear programming problem. In
standard form, linear programming problems assume the variables x are
non-negative. Since the variables don't have standard bounds where
0 <= x <= inf, the bounds of the variables must be explicitly set.
There are two upper-bound constraints, which can be expressed as
dot(A_ub, x) <= b_ub
The input for this problem is as follows:
>>> from scipy.optimize import linprog
>>> c = [-1, 4]
>>> A = [[-3, 1], [1, 2]]
>>> b = [6, 4]
>>> x0_bnds = (None, None)
>>> x1_bnds = (-3, None)
>>> res = linprog(c, A, b, bounds=(x0_bnds, x1_bnds))
>>> print(res)
fun: -22.0
message: 'Optimization terminated successfully.'
nit: 1
slack: array([ 39., 0.])
status: 0
success: True
x: array([ 10., -3.])
References
----------
.. [1] Dantzig, George B., Linear programming and extensions. Rand
Corporation Research Study Princeton Univ. Press, Princeton, NJ,
1963
.. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to
Mathematical Programming", McGraw-Hill, Chapter 4.
.. [3] Bland, Robert G. New finite pivoting rules for the simplex method.
Mathematics of Operations Research (2), 1977: pp. 103-107.
"""
_check_unknown_options(unknown_options)
status = 0
messages = {0: "Optimization terminated successfully.",
1: "Iteration limit reached.",
2: "Optimization failed. Unable to find a feasible"
" starting point.",
3: "Optimization failed. The problem appears to be unbounded.",
4: "Optimization failed. Singular matrix encountered."}
have_floor_variable = False
cc = np.asarray(c)
# The initial value of the objective function element in the tableau
f0 = 0
# The number of variables as given by c
n = len(c)
# Convert the input arguments to arrays (sized to zero if not provided)
Aeq = np.asarray(A_eq) if A_eq is not None else np.empty([0, len(cc)])
Aub = np.asarray(A_ub) if A_ub is not None else np.empty([0, len(cc)])
beq = np.ravel(np.asarray(b_eq)) if b_eq is not None else np.empty([0])
bub = np.ravel(np.asarray(b_ub)) if b_ub is not None else np.empty([0])
# Analyze the bounds and determine what modifications to be made to
# the constraints in order to accommodate them.
L = np.zeros(n, dtype=np.float64)
U = np.ones(n, dtype=np.float64)*np.inf
if bounds is None or len(bounds) == 0:
pass
elif len(bounds) == 2 and not hasattr(bounds[0], '__len__'):
# All bounds are the same
a = bounds[0] if bounds[0] is not None else -np.inf
b = bounds[1] if bounds[1] is not None else np.inf
L = np.asarray(n*[a], dtype=np.float64)
U = np.asarray(n*[b], dtype=np.float64)
else:
if len(bounds) != n:
status = -1
message = ("Invalid input for linprog with method = 'simplex'. "
"Length of bounds is inconsistent with the length of c")
else:
try:
for i in range(n):
if len(bounds[i]) != 2:
raise IndexError()
L[i] = bounds[i][0] if bounds[i][0] is not None else -np.inf
U[i] = bounds[i][1] if bounds[i][1] is not None else np.inf
except IndexError:
status = -1
message = ("Invalid input for linprog with "
"method = 'simplex'. bounds must be a n x 2 "
"sequence/array where n = len(c).")
if np.any(L == -np.inf):
# If any lower-bound constraint is a free variable
# add the first column variable as the "floor" variable which
# accommodates the most negative variable in the problem.
n = n + 1
L = np.concatenate([np.array([0]), L])
U = np.concatenate([np.array([np.inf]), U])
cc = np.concatenate([np.array([0]), cc])
Aeq = np.hstack([np.zeros([Aeq.shape[0], 1]), Aeq])
Aub = np.hstack([np.zeros([Aub.shape[0], 1]), Aub])
have_floor_variable = True
# Now before we deal with any variables with lower bounds < 0,
# deal with finite bounds which can be simply added as new constraints.
# Also validate bounds inputs here.
for i in range(n):
if(L[i] > U[i]):
status = -1
message = ("Invalid input for linprog with method = 'simplex'. "
"Lower bound %d is greater than upper bound%d" % (i, i))
if np.isinf(L[i]) and L[i] > 0:
status = -1
message = ("Invalid input for linprog with method = 'simplex'. "
"Lower bound may not be +infinity")
if np.isinf(U[i]) and U[i] < 0:
status = -1
message = ("Invalid input for linprog with method = 'simplex'. "
"Upper bound may not be -infinity")
if np.isfinite(L[i]) and L[i] > 0:
# Add a new lower-bound (negative upper-bound) constraint
Aub = np.vstack([Aub, np.zeros(n)])
Aub[-1, i] = -1
bub = np.concatenate([bub, np.array([-L[i]])])
L[i] = 0
if np.isfinite(U[i]):
# Add a new upper-bound constraint
Aub = np.vstack([Aub, np.zeros(n)])
Aub[-1, i] = 1
bub = np.concatenate([bub, np.array([U[i]])])
U[i] = np.inf
# Now find negative lower bounds (finite or infinite) which require a
# change of variables or free variables and handle them appropriately
for i in range(0, n):
if L[i] < 0:
if np.isfinite(L[i]) and L[i] < 0:
# Add a change of variables for x[i]
# For each row in the constraint matrices, we take the
# coefficient from column i in A,
# and subtract the product of that and L[i] to the RHS b
beq = beq - Aeq[:, i] * L[i]
bub = bub - Aub[:, i] * L[i]
# We now have a nonzero initial value for the objective
# function as well.
f0 = f0 - cc[i] * L[i]
else:
# This is an unrestricted variable, let x[i] = u[i] - v[0]
# where v is the first column in all matrices.
Aeq[:, 0] = Aeq[:, 0] - Aeq[:, i]
Aub[:, 0] = Aub[:, 0] - Aub[:, i]
cc[0] = cc[0] - cc[i]
if np.isinf(U[i]):
if U[i] < 0:
status = -1
message = ("Invalid input for linprog with "
"method = 'simplex'. Upper bound may not be -inf.")
# The number of upper bound constraints (rows in A_ub and elements in b_ub)
mub = len(bub)
# The number of equality constraints (rows in A_eq and elements in b_eq)
meq = len(beq)
# The total number of constraints
m = mub+meq
# The number of slack variables (one for each upper-bound constraints)
n_slack = mub
# The number of artificial variables (one for each lower-bound and equality
# constraint)
n_artificial = meq + np.count_nonzero(bub < 0)
try:
Aub_rows, Aub_cols = Aub.shape
except ValueError:
raise ValueError("Invalid input. A_ub must be two-dimensional")
try:
Aeq_rows, Aeq_cols = Aeq.shape
except ValueError:
raise ValueError("Invalid input. A_eq must be two-dimensional")
if Aeq_rows != meq:
status = -1
message = ("Invalid input for linprog with method = 'simplex'. "
"The number of rows in A_eq must be equal "
"to the number of values in b_eq")
if Aub_rows != mub:
status = -1
message = ("Invalid input for linprog with method = 'simplex'. "
"The number of rows in A_ub must be equal "
"to the number of values in b_ub")
if Aeq_cols > 0 and Aeq_cols != n:
status = -1
message = ("Invalid input for linprog with method = 'simplex'. "
"Number of columns in A_eq must be equal "
"to the size of c")
if Aub_cols > 0 and Aub_cols != n:
status = -1
message = ("Invalid input for linprog with method = 'simplex'. "
"Number of columns in A_ub must be equal to the size of c")
if status != 0:
# Invalid inputs provided
raise ValueError(message)
# Create the tableau
T = np.zeros([m+2, n+n_slack+n_artificial+1])
# Insert objective into tableau
T[-2, :n] = cc
T[-2, -1] = f0
b = T[:-2, -1]
if meq > 0:
# Add Aeq to the tableau
T[:meq, :n] = Aeq
# Add beq to the tableau
b[:meq] = beq
if mub > 0:
# Add Aub to the tableau
T[meq:meq+mub, :n] = Aub
# At bub to the tableau
b[meq:meq+mub] = bub
# Add the slack variables to the tableau
np.fill_diagonal(T[meq:m, n:n+n_slack], 1)
# Further set up the tableau.
# If a row corresponds to an equality constraint or a negative b (a lower
# bound constraint), then an artificial variable is added for that row.
# Also, if b is negative, first flip the signs in that constraint.
slcount = 0
avcount = 0
basis = np.zeros(m, dtype=int)
r_artificial = np.zeros(n_artificial, dtype=int)
for i in range(m):
if i < meq or b[i] < 0:
# basic variable i is in column n+n_slack+avcount
basis[i] = n+n_slack+avcount
r_artificial[avcount] = i
avcount += 1
if b[i] < 0:
b[i] *= -1
T[i, :-1] *= -1
T[i, basis[i]] = 1
T[-1, basis[i]] = 1
else:
# basic variable i is in column n+slcount
basis[i] = n+slcount
slcount += 1
# Make the artificial variables basic feasible variables by subtracting
# each row with an artificial variable from the Phase 1 objective
for r in r_artificial:
T[-1, :] = T[-1, :] - T[r, :]
nit1, status = _solve_simplex(T, n, basis, phase=1, callback=callback,
maxiter=maxiter, tol=tol, bland=bland)
# if pseudo objective is zero, remove the last row from the tableau and
# proceed to phase 2
if abs(T[-1, -1]) < tol:
# Remove the pseudo-objective row from the tableau
T = T[:-1, :]
# Remove the artificial variable columns from the tableau
T = np.delete(T, np.s_[n+n_slack:n+n_slack+n_artificial], 1)
else:
# Failure to find a feasible starting point
status = 2
if status != 0:
message = messages[status]
if disp:
print(message)
return OptimizeResult(x=np.nan, fun=-T[-1, -1], nit=nit1,
status=status, message=message, success=False)
# Phase 2
nit2, status = _solve_simplex(T, n, basis, maxiter=maxiter-nit1, phase=2,
callback=callback, tol=tol, nit0=nit1,
bland=bland)
solution = np.zeros(n+n_slack+n_artificial)
solution[basis[:m]] = T[:m, -1]
x = solution[:n]
slack = solution[n:n+n_slack]
# For those variables with finite negative lower bounds,
# reverse the change of variables
masked_L = np.ma.array(L, mask=np.isinf(L), fill_value=0.0).filled()
x = x + masked_L
# For those variables with infinite negative lower bounds,
# take x[i] as the difference between x[i] and the floor variable.
if have_floor_variable:
for i in range(1, n):
if np.isinf(L[i]):
x[i] -= x[0]
x = x[1:]
# Optimization complete at this point
obj = -T[-1, -1]
if status in (0, 1):
if disp:
print(messages[status])
print(" Current function value: {0: <12.6f}".format(obj))
print(" Iterations: {0:d}".format(nit2))
else:
if disp:
print(messages[status])
print(" Iterations: {0:d}".format(nit2))
return OptimizeResult(x=x, fun=obj, nit=int(nit2), status=status,
slack=slack, message=messages[status],
success=(status == 0))
def linprog(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None,
bounds=None, method='simplex', callback=None,
options=None):
"""
Minimize a linear objective function subject to linear
equality and inequality constraints.
Linear Programming is intended to solve the following problem form::
Minimize: c^T * x
Subject to: A_ub * x <= b_ub
A_eq * x == b_eq
Parameters
----------
c : array_like
Coefficients of the linear objective function to be minimized.
A_ub : array_like, optional
2-D array which, when matrix-multiplied by ``x``, gives the values of
the upper-bound inequality constraints at ``x``.
b_ub : array_like, optional
1-D array of values representing the upper-bound of each inequality
constraint (row) in ``A_ub``.
A_eq : array_like, optional
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x``.
b_eq : array_like, optional
1-D array of values representing the RHS of each equality constraint
(row) in ``A_eq``.
bounds : sequence, optional
``(min, max)`` pairs for each element in ``x``, defining
the bounds on that parameter. Use None for one of ``min`` or
``max`` when there is no bound in that direction. By default
bounds are ``(0, None)`` (non-negative)
If a sequence containing a single tuple is provided, then ``min`` and
``max`` will be applied to all variables in the problem.
method : str, optional
Type of solver. :ref:`'simplex' <optimize.linprog-simplex>`
and :ref:`'interior-point' <optimize.linprog-interior-point>`
are supported.
callback : callable, optional (simplex only)
If a callback function is provide, it will be called within each
iteration of the simplex algorithm. The callback must have the
signature ``callback(xk, **kwargs)`` where ``xk`` is the current
solution vector and ``kwargs`` is a dictionary containing the
following::
"tableau" : The current Simplex algorithm tableau
"nit" : The current iteration.
"pivot" : The pivot (row, column) used for the next iteration.
"phase" : Whether the algorithm is in Phase 1 or Phase 2.
"basis" : The indices of the columns of the basic variables.
options : dict, optional
A dictionary of solver options. All methods accept the following
generic options:
maxiter : int
Maximum number of iterations to perform.
disp : bool
Set to True to print convergence messages.
For method-specific options, see :func:`show_options('linprog')`.
Returns
-------
A `scipy.optimize.OptimizeResult` consisting of the following fields:
x : ndarray
The independent variable vector which optimizes the linear
programming problem.
fun : float
Value of the objective function.
slack : ndarray
The values of the slack variables. Each slack variable corresponds
to an inequality constraint. If the slack is zero, then the
corresponding constraint is active.
success : bool
Returns True if the algorithm succeeded in finding an optimal
solution.
status : int
An integer representing the exit status of the optimization::
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
nit : int
The number of iterations performed.
message : str
A string descriptor of the exit status of the optimization.
See Also
--------
show_options : Additional options accepted by the solvers
Notes
-----
This section describes the available solvers that can be selected by the
'method' parameter. The default method
is :ref:`Simplex <optimize.linprog-simplex>`.
:ref:`Interior point <optimize.linprog-interior-point>` is also available.
Method *simplex* uses the simplex algorithm (as it relates to linear
programming, NOT the Nelder-Mead simplex) [1]_, [2]_. This algorithm
should be reasonably reliable and fast for small problems.
.. versionadded:: 0.15.0
Method *interior-point* uses the primal-dual path following algorithm
as outlined in [4]_. This algorithm is intended to provide a faster
and more reliable alternative to *simplex*, especially for large,
sparse problems. Note, however, that the solution returned may be slightly
less accurate than that of the simplex method and may not correspond with a
vertex of the polytope defined by the constraints.
References
----------
.. [1] Dantzig, George B., Linear programming and extensions. Rand
Corporation Research Study Princeton Univ. Press, Princeton, NJ,
1963
.. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to
Mathematical Programming", McGraw-Hill, Chapter 4.
.. [3] Bland, Robert G. New finite pivoting rules for the simplex method.
Mathematics of Operations Research (2), 1977: pp. 103-107.
.. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
.. [5] Andersen, Erling D. "Finding all linearly dependent rows in
large-scale linear programming." Optimization Methods and Software
6.3 (1995): 219-227.
.. [6] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear
Programming based on Newton's Method." Unpublished Course Notes,
March 2004. Available 2/25/2017 at
https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf
.. [7] Fourer, Robert. "Solving Linear Programs by Interior-Point Methods."
Unpublished Course Notes, August 26, 2005. Available 2/25/2017 at
http://www.4er.org/CourseNotes/Book%20B/B-III.pdf
.. [8] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear
programming." Mathematical Programming 71.2 (1995): 221-245.
.. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear
programming." Athena Scientific 1 (1997): 997.
.. [10] Andersen, Erling D., et al. Implementation of interior point
methods for large scale linear programming. HEC/Universite de
Geneve, 1996.
Examples
--------
Consider the following problem:
Minimize: f = -1*x[0] + 4*x[1]
Subject to: -3*x[0] + 1*x[1] <= 6
1*x[0] + 2*x[1] <= 4
x[1] >= -3
where: -inf <= x[0] <= inf
This problem deviates from the standard linear programming problem.
In standard form, linear programming problems assume the variables x are
non-negative. Since the variables don't have standard bounds where
0 <= x <= inf, the bounds of the variables must be explicitly set.
There are two upper-bound constraints, which can be expressed as
dot(A_ub, x) <= b_ub
The input for this problem is as follows:
>>> c = [-1, 4]
>>> A = [[-3, 1], [1, 2]]
>>> b = [6, 4]
>>> x0_bounds = (None, None)
>>> x1_bounds = (-3, None)
>>> from scipy.optimize import linprog
>>> res = linprog(c, A_ub=A, b_ub=b, bounds=(x0_bounds, x1_bounds),
... options={"disp": True})
Optimization terminated successfully.
Current function value: -22.000000
Iterations: 1
>>> print(res)
fun: -22.0
message: 'Optimization terminated successfully.'
nit: 1
slack: array([39., 0.])
status: 0
success: True
x: array([10., -3.])
Note the actual objective value is 11.428571. In this case we minimized
the negative of the objective function.
"""
meth = method.lower()
if options is None:
options = {}
if meth == 'simplex':
return _linprog_simplex(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq,
bounds=bounds, callback=callback, **options)
elif meth == 'interior-point':
return _linprog_ip(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq,
bounds=bounds, callback=callback, **options)
else:
raise ValueError('Unknown solver %s' % method)
| 40,117 | 37.244042 | 143 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_hungarian.py
|
# Hungarian algorithm (Kuhn-Munkres) for solving the linear sum assignment
# problem. Taken from scikit-learn. Based on original code by Brian Clapper,
# adapted to NumPy by Gael Varoquaux.
# Further improvements by Ben Root, Vlad Niculae and Lars Buitinck.
#
# Copyright (c) 2008 Brian M. Clapper <bmc@clapper.org>, Gael Varoquaux
# Author: Brian M. Clapper, Gael Varoquaux
# License: 3-clause BSD
import numpy as np
def linear_sum_assignment(cost_matrix):
"""Solve the linear sum assignment problem.
The linear sum assignment problem is also known as minimum weight matching
in bipartite graphs. A problem instance is described by a matrix C, where
each C[i,j] is the cost of matching vertex i of the first partite set
(a "worker") and vertex j of the second set (a "job"). The goal is to find
a complete assignment of workers to jobs of minimal cost.
Formally, let X be a boolean matrix where :math:`X[i,j] = 1` iff row i is
assigned to column j. Then the optimal assignment has cost
.. math::
\\min \\sum_i \\sum_j C_{i,j} X_{i,j}
s.t. each row is assignment to at most one column, and each column to at
most one row.
This function can also solve a generalization of the classic assignment
problem where the cost matrix is rectangular. If it has more rows than
columns, then not every row needs to be assigned to a column, and vice
versa.
The method used is the Hungarian algorithm, also known as the Munkres or
Kuhn-Munkres algorithm.
Parameters
----------
cost_matrix : array
The cost matrix of the bipartite graph.
Returns
-------
row_ind, col_ind : array
An array of row indices and one of corresponding column indices giving
the optimal assignment. The cost of the assignment can be computed
as ``cost_matrix[row_ind, col_ind].sum()``. The row indices will be
sorted; in the case of a square cost matrix they will be equal to
``numpy.arange(cost_matrix.shape[0])``.
Notes
-----
.. versionadded:: 0.17.0
Examples
--------
>>> cost = np.array([[4, 1, 3], [2, 0, 5], [3, 2, 2]])
>>> from scipy.optimize import linear_sum_assignment
>>> row_ind, col_ind = linear_sum_assignment(cost)
>>> col_ind
array([1, 0, 2])
>>> cost[row_ind, col_ind].sum()
5
References
----------
1. http://csclab.murraystate.edu/bob.pilgrim/445/munkres.html
2. Harold W. Kuhn. The Hungarian Method for the assignment problem.
*Naval Research Logistics Quarterly*, 2:83-97, 1955.
3. Harold W. Kuhn. Variants of the Hungarian method for assignment
problems. *Naval Research Logistics Quarterly*, 3: 253-258, 1956.
4. Munkres, J. Algorithms for the Assignment and Transportation Problems.
*J. SIAM*, 5(1):32-38, March, 1957.
5. https://en.wikipedia.org/wiki/Hungarian_algorithm
"""
cost_matrix = np.asarray(cost_matrix)
if len(cost_matrix.shape) != 2:
raise ValueError("expected a matrix (2-d array), got a %r array"
% (cost_matrix.shape,))
if not (np.issubdtype(cost_matrix.dtype, np.number) or
cost_matrix.dtype == np.dtype(np.bool)):
raise ValueError("expected a matrix containing numerical entries, got %s"
% (cost_matrix.dtype,))
if np.any(np.isinf(cost_matrix) | np.isnan(cost_matrix)):
raise ValueError("matrix contains invalid numeric entries")
if cost_matrix.dtype == np.dtype(np.bool):
cost_matrix = cost_matrix.astype(np.int)
# The algorithm expects more columns than rows in the cost matrix.
if cost_matrix.shape[1] < cost_matrix.shape[0]:
cost_matrix = cost_matrix.T
transposed = True
else:
transposed = False
state = _Hungary(cost_matrix)
# No need to bother with assignments if one of the dimensions
# of the cost matrix is zero-length.
step = None if 0 in cost_matrix.shape else _step1
while step is not None:
step = step(state)
if transposed:
marked = state.marked.T
else:
marked = state.marked
return np.where(marked == 1)
class _Hungary(object):
"""State of the Hungarian algorithm.
Parameters
----------
cost_matrix : 2D matrix
The cost matrix. Must have shape[1] >= shape[0].
"""
def __init__(self, cost_matrix):
self.C = cost_matrix.copy()
n, m = self.C.shape
self.row_uncovered = np.ones(n, dtype=bool)
self.col_uncovered = np.ones(m, dtype=bool)
self.Z0_r = 0
self.Z0_c = 0
self.path = np.zeros((n + m, 2), dtype=int)
self.marked = np.zeros((n, m), dtype=int)
def _clear_covers(self):
"""Clear all covered matrix cells"""
self.row_uncovered[:] = True
self.col_uncovered[:] = True
# Individual steps of the algorithm follow, as a state machine: they return
# the next step to be taken (function to be called), if any.
def _step1(state):
"""Steps 1 and 2 in the Wikipedia page."""
# Step 1: For each row of the matrix, find the smallest element and
# subtract it from every element in its row.
state.C -= state.C.min(axis=1)[:, np.newaxis]
# Step 2: Find a zero (Z) in the resulting matrix. If there is no
# starred zero in its row or column, star Z. Repeat for each element
# in the matrix.
for i, j in zip(*np.where(state.C == 0)):
if state.col_uncovered[j] and state.row_uncovered[i]:
state.marked[i, j] = 1
state.col_uncovered[j] = False
state.row_uncovered[i] = False
state._clear_covers()
return _step3
def _step3(state):
"""
Cover each column containing a starred zero. If n columns are covered,
the starred zeros describe a complete set of unique assignments.
In this case, Go to DONE, otherwise, Go to Step 4.
"""
marked = (state.marked == 1)
state.col_uncovered[np.any(marked, axis=0)] = False
if marked.sum() < state.C.shape[0]:
return _step4
def _step4(state):
"""
Find a noncovered zero and prime it. If there is no starred zero
in the row containing this primed zero, Go to Step 5. Otherwise,
cover this row and uncover the column containing the starred
zero. Continue in this manner until there are no uncovered zeros
left. Save the smallest uncovered value and Go to Step 6.
"""
# We convert to int as numpy operations are faster on int
C = (state.C == 0).astype(int)
covered_C = C * state.row_uncovered[:, np.newaxis]
covered_C *= np.asarray(state.col_uncovered, dtype=int)
n = state.C.shape[0]
m = state.C.shape[1]
while True:
# Find an uncovered zero
row, col = np.unravel_index(np.argmax(covered_C), (n, m))
if covered_C[row, col] == 0:
return _step6
else:
state.marked[row, col] = 2
# Find the first starred element in the row
star_col = np.argmax(state.marked[row] == 1)
if state.marked[row, star_col] != 1:
# Could not find one
state.Z0_r = row
state.Z0_c = col
return _step5
else:
col = star_col
state.row_uncovered[row] = False
state.col_uncovered[col] = True
covered_C[:, col] = C[:, col] * (
np.asarray(state.row_uncovered, dtype=int))
covered_C[row] = 0
def _step5(state):
"""
Construct a series of alternating primed and starred zeros as follows.
Let Z0 represent the uncovered primed zero found in Step 4.
Let Z1 denote the starred zero in the column of Z0 (if any).
Let Z2 denote the primed zero in the row of Z1 (there will always be one).
Continue until the series terminates at a primed zero that has no starred
zero in its column. Unstar each starred zero of the series, star each
primed zero of the series, erase all primes and uncover every line in the
matrix. Return to Step 3
"""
count = 0
path = state.path
path[count, 0] = state.Z0_r
path[count, 1] = state.Z0_c
while True:
# Find the first starred element in the col defined by
# the path.
row = np.argmax(state.marked[:, path[count, 1]] == 1)
if state.marked[row, path[count, 1]] != 1:
# Could not find one
break
else:
count += 1
path[count, 0] = row
path[count, 1] = path[count - 1, 1]
# Find the first prime element in the row defined by the
# first path step
col = np.argmax(state.marked[path[count, 0]] == 2)
if state.marked[row, col] != 2:
col = -1
count += 1
path[count, 0] = path[count - 1, 0]
path[count, 1] = col
# Convert paths
for i in range(count + 1):
if state.marked[path[i, 0], path[i, 1]] == 1:
state.marked[path[i, 0], path[i, 1]] = 0
else:
state.marked[path[i, 0], path[i, 1]] = 1
state._clear_covers()
# Erase all prime markings
state.marked[state.marked == 2] = 0
return _step3
def _step6(state):
"""
Add the value found in Step 4 to every element of each covered row,
and subtract it from every element of each uncovered column.
Return to Step 4 without altering any stars, primes, or covered lines.
"""
# the smallest uncovered value in the matrix
if np.any(state.row_uncovered) and np.any(state.col_uncovered):
minval = np.min(state.C[state.row_uncovered], axis=0)
minval = np.min(minval[state.col_uncovered])
state.C[~state.row_uncovered] += minval
state.C[:, state.col_uncovered] -= minval
return _step4
| 9,854 | 33.823322 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/tnc.py
|
# TNC Python interface
# @(#) $Jeannot: tnc.py,v 1.11 2005/01/28 18:27:31 js Exp $
# Copyright (c) 2004-2005, Jean-Sebastien Roy (js@jeannot.org)
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the
# "Software"), to deal in the Software without restriction, including
# without limitation the rights to use, copy, modify, merge, publish,
# distribute, sublicense, and/or sell copies of the Software, and to
# permit persons to whom the Software is furnished to do so, subject to
# the following conditions:
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
"""
TNC: A python interface to the TNC non-linear optimizer
TNC is a non-linear optimizer. To use it, you must provide a function to
minimize. The function must take one argument: the list of coordinates where to
evaluate the function; and it must return either a tuple, whose first element is the
value of the function, and whose second argument is the gradient of the function
(as a list of values); or None, to abort the minimization.
"""
from __future__ import division, print_function, absolute_import
from scipy.optimize import moduleTNC, approx_fprime
from .optimize import MemoizeJac, OptimizeResult, _check_unknown_options
from numpy import inf, array, zeros, asfarray
__all__ = ['fmin_tnc']
MSG_NONE = 0 # No messages
MSG_ITER = 1 # One line per iteration
MSG_INFO = 2 # Informational messages
MSG_VERS = 4 # Version info
MSG_EXIT = 8 # Exit reasons
MSG_ALL = MSG_ITER + MSG_INFO + MSG_VERS + MSG_EXIT
MSGS = {
MSG_NONE: "No messages",
MSG_ITER: "One line per iteration",
MSG_INFO: "Informational messages",
MSG_VERS: "Version info",
MSG_EXIT: "Exit reasons",
MSG_ALL: "All messages"
}
INFEASIBLE = -1 # Infeasible (lower bound > upper bound)
LOCALMINIMUM = 0 # Local minimum reached (|pg| ~= 0)
FCONVERGED = 1 # Converged (|f_n-f_(n-1)| ~= 0)
XCONVERGED = 2 # Converged (|x_n-x_(n-1)| ~= 0)
MAXFUN = 3 # Max. number of function evaluations reached
LSFAIL = 4 # Linear search failed
CONSTANT = 5 # All lower bounds are equal to the upper bounds
NOPROGRESS = 6 # Unable to progress
USERABORT = 7 # User requested end of minimization
RCSTRINGS = {
INFEASIBLE: "Infeasible (lower bound > upper bound)",
LOCALMINIMUM: "Local minimum reached (|pg| ~= 0)",
FCONVERGED: "Converged (|f_n-f_(n-1)| ~= 0)",
XCONVERGED: "Converged (|x_n-x_(n-1)| ~= 0)",
MAXFUN: "Max. number of function evaluations reached",
LSFAIL: "Linear search failed",
CONSTANT: "All lower bounds are equal to the upper bounds",
NOPROGRESS: "Unable to progress",
USERABORT: "User requested end of minimization"
}
# Changes to interface made by Travis Oliphant, Apr. 2004 for inclusion in
# SciPy
def fmin_tnc(func, x0, fprime=None, args=(), approx_grad=0,
bounds=None, epsilon=1e-8, scale=None, offset=None,
messages=MSG_ALL, maxCGit=-1, maxfun=None, eta=-1,
stepmx=0, accuracy=0, fmin=0, ftol=-1, xtol=-1, pgtol=-1,
rescale=-1, disp=None, callback=None):
"""
Minimize a function with variables subject to bounds, using
gradient information in a truncated Newton algorithm. This
method wraps a C implementation of the algorithm.
Parameters
----------
func : callable ``func(x, *args)``
Function to minimize. Must do one of:
1. Return f and g, where f is the value of the function and g its
gradient (a list of floats).
2. Return the function value but supply gradient function
separately as `fprime`.
3. Return the function value and set ``approx_grad=True``.
If the function returns None, the minimization
is aborted.
x0 : array_like
Initial estimate of minimum.
fprime : callable ``fprime(x, *args)``, optional
Gradient of `func`. If None, then either `func` must return the
function value and the gradient (``f,g = func(x, *args)``)
or `approx_grad` must be True.
args : tuple, optional
Arguments to pass to function.
approx_grad : bool, optional
If true, approximate the gradient numerically.
bounds : list, optional
(min, max) pairs for each element in x0, defining the
bounds on that parameter. Use None or +/-inf for one of
min or max when there is no bound in that direction.
epsilon : float, optional
Used if approx_grad is True. The stepsize in a finite
difference approximation for fprime.
scale : array_like, optional
Scaling factors to apply to each variable. If None, the
factors are up-low for interval bounded variables and
1+|x| for the others. Defaults to None.
offset : array_like, optional
Value to subtract from each variable. If None, the
offsets are (up+low)/2 for interval bounded variables
and x for the others.
messages : int, optional
Bit mask used to select messages display during
minimization values defined in the MSGS dict. Defaults to
MGS_ALL.
disp : int, optional
Integer interface to messages. 0 = no message, 5 = all messages
maxCGit : int, optional
Maximum number of hessian*vector evaluations per main
iteration. If maxCGit == 0, the direction chosen is
-gradient if maxCGit < 0, maxCGit is set to
max(1,min(50,n/2)). Defaults to -1.
maxfun : int, optional
Maximum number of function evaluation. if None, maxfun is
set to max(100, 10*len(x0)). Defaults to None.
eta : float, optional
Severity of the line search. if < 0 or > 1, set to 0.25.
Defaults to -1.
stepmx : float, optional
Maximum step for the line search. May be increased during
call. If too small, it will be set to 10.0. Defaults to 0.
accuracy : float, optional
Relative precision for finite difference calculations. If
<= machine_precision, set to sqrt(machine_precision).
Defaults to 0.
fmin : float, optional
Minimum function value estimate. Defaults to 0.
ftol : float, optional
Precision goal for the value of f in the stopping criterion.
If ftol < 0.0, ftol is set to 0.0 defaults to -1.
xtol : float, optional
Precision goal for the value of x in the stopping
criterion (after applying x scaling factors). If xtol <
0.0, xtol is set to sqrt(machine_precision). Defaults to
-1.
pgtol : float, optional
Precision goal for the value of the projected gradient in
the stopping criterion (after applying x scaling factors).
If pgtol < 0.0, pgtol is set to 1e-2 * sqrt(accuracy).
Setting it to 0.0 is not recommended. Defaults to -1.
rescale : float, optional
Scaling factor (in log10) used to trigger f value
rescaling. If 0, rescale at each iteration. If a large
value, never rescale. If < 0, rescale is set to 1.3.
callback : callable, optional
Called after each iteration, as callback(xk), where xk is the
current parameter vector.
Returns
-------
x : ndarray
The solution.
nfeval : int
The number of function evaluations.
rc : int
Return code, see below
See also
--------
minimize: Interface to minimization algorithms for multivariate
functions. See the 'TNC' `method` in particular.
Notes
-----
The underlying algorithm is truncated Newton, also called
Newton Conjugate-Gradient. This method differs from
scipy.optimize.fmin_ncg in that
1. It wraps a C implementation of the algorithm
2. It allows each variable to be given an upper and lower bound.
The algorithm incorporates the bound constraints by determining
the descent direction as in an unconstrained truncated Newton,
but never taking a step-size large enough to leave the space
of feasible x's. The algorithm keeps track of a set of
currently active constraints, and ignores them when computing
the minimum allowable step size. (The x's associated with the
active constraint are kept fixed.) If the maximum allowable
step size is zero then a new constraint is added. At the end
of each iteration one of the constraints may be deemed no
longer active and removed. A constraint is considered
no longer active is if it is currently active
but the gradient for that variable points inward from the
constraint. The specific constraint removed is the one
associated with the variable of largest index whose
constraint is no longer active.
Return codes are defined as follows::
-1 : Infeasible (lower bound > upper bound)
0 : Local minimum reached (|pg| ~= 0)
1 : Converged (|f_n-f_(n-1)| ~= 0)
2 : Converged (|x_n-x_(n-1)| ~= 0)
3 : Max. number of function evaluations reached
4 : Linear search failed
5 : All lower bounds are equal to the upper bounds
6 : Unable to progress
7 : User requested end of minimization
References
----------
Wright S., Nocedal J. (2006), 'Numerical Optimization'
Nash S.G. (1984), "Newton-Type Minimization Via the Lanczos Method",
SIAM Journal of Numerical Analysis 21, pp. 770-778
"""
# handle fprime/approx_grad
if approx_grad:
fun = func
jac = None
elif fprime is None:
fun = MemoizeJac(func)
jac = fun.derivative
else:
fun = func
jac = fprime
if disp is not None: # disp takes precedence over messages
mesg_num = disp
else:
mesg_num = {0:MSG_NONE, 1:MSG_ITER, 2:MSG_INFO, 3:MSG_VERS,
4:MSG_EXIT, 5:MSG_ALL}.get(messages, MSG_ALL)
# build options
opts = {'eps': epsilon,
'scale': scale,
'offset': offset,
'mesg_num': mesg_num,
'maxCGit': maxCGit,
'maxiter': maxfun,
'eta': eta,
'stepmx': stepmx,
'accuracy': accuracy,
'minfev': fmin,
'ftol': ftol,
'xtol': xtol,
'gtol': pgtol,
'rescale': rescale,
'disp': False}
res = _minimize_tnc(fun, x0, args, jac, bounds, callback=callback, **opts)
return res['x'], res['nfev'], res['status']
def _minimize_tnc(fun, x0, args=(), jac=None, bounds=None,
eps=1e-8, scale=None, offset=None, mesg_num=None,
maxCGit=-1, maxiter=None, eta=-1, stepmx=0, accuracy=0,
minfev=0, ftol=-1, xtol=-1, gtol=-1, rescale=-1, disp=False,
callback=None, **unknown_options):
"""
Minimize a scalar function of one or more variables using a truncated
Newton (TNC) algorithm.
Options
-------
eps : float
Step size used for numerical approximation of the jacobian.
scale : list of floats
Scaling factors to apply to each variable. If None, the
factors are up-low for interval bounded variables and
1+|x] fo the others. Defaults to None
offset : float
Value to subtract from each variable. If None, the
offsets are (up+low)/2 for interval bounded variables
and x for the others.
disp : bool
Set to True to print convergence messages.
maxCGit : int
Maximum number of hessian*vector evaluations per main
iteration. If maxCGit == 0, the direction chosen is
-gradient if maxCGit < 0, maxCGit is set to
max(1,min(50,n/2)). Defaults to -1.
maxiter : int
Maximum number of function evaluation. if None, `maxiter` is
set to max(100, 10*len(x0)). Defaults to None.
eta : float
Severity of the line search. if < 0 or > 1, set to 0.25.
Defaults to -1.
stepmx : float
Maximum step for the line search. May be increased during
call. If too small, it will be set to 10.0. Defaults to 0.
accuracy : float
Relative precision for finite difference calculations. If
<= machine_precision, set to sqrt(machine_precision).
Defaults to 0.
minfev : float
Minimum function value estimate. Defaults to 0.
ftol : float
Precision goal for the value of f in the stopping criterion.
If ftol < 0.0, ftol is set to 0.0 defaults to -1.
xtol : float
Precision goal for the value of x in the stopping
criterion (after applying x scaling factors). If xtol <
0.0, xtol is set to sqrt(machine_precision). Defaults to
-1.
gtol : float
Precision goal for the value of the projected gradient in
the stopping criterion (after applying x scaling factors).
If gtol < 0.0, gtol is set to 1e-2 * sqrt(accuracy).
Setting it to 0.0 is not recommended. Defaults to -1.
rescale : float
Scaling factor (in log10) used to trigger f value
rescaling. If 0, rescale at each iteration. If a large
value, never rescale. If < 0, rescale is set to 1.3.
"""
_check_unknown_options(unknown_options)
epsilon = eps
maxfun = maxiter
fmin = minfev
pgtol = gtol
x0 = asfarray(x0).flatten()
n = len(x0)
if bounds is None:
bounds = [(None,None)] * n
if len(bounds) != n:
raise ValueError('length of x0 != length of bounds')
if mesg_num is not None:
messages = {0:MSG_NONE, 1:MSG_ITER, 2:MSG_INFO, 3:MSG_VERS,
4:MSG_EXIT, 5:MSG_ALL}.get(mesg_num, MSG_ALL)
elif disp:
messages = MSG_ALL
else:
messages = MSG_NONE
if jac is None:
def func_and_grad(x):
f = fun(x, *args)
g = approx_fprime(x, fun, epsilon, *args)
return f, g
else:
def func_and_grad(x):
f = fun(x, *args)
g = jac(x, *args)
return f, g
"""
low, up : the bounds (lists of floats)
if low is None, the lower bounds are removed.
if up is None, the upper bounds are removed.
low and up defaults to None
"""
low = zeros(n)
up = zeros(n)
for i in range(n):
if bounds[i] is None:
l, u = -inf, inf
else:
l,u = bounds[i]
if l is None:
low[i] = -inf
else:
low[i] = l
if u is None:
up[i] = inf
else:
up[i] = u
if scale is None:
scale = array([])
if offset is None:
offset = array([])
if maxfun is None:
maxfun = max(100, 10*len(x0))
rc, nf, nit, x = moduleTNC.minimize(func_and_grad, x0, low, up, scale,
offset, messages, maxCGit, maxfun,
eta, stepmx, accuracy, fmin, ftol,
xtol, pgtol, rescale, callback)
funv, jacv = func_and_grad(x)
return OptimizeResult(x=x, fun=funv, jac=jacv, nfev=nf, nit=nit, status=rc,
message=RCSTRINGS[rc], success=(-1 < rc < 3))
if __name__ == '__main__':
# Examples for TNC
def example():
print("Example")
# A function to minimize
def function(x):
f = pow(x[0],2.0)+pow(abs(x[1]),3.0)
g = [0,0]
g[0] = 2.0*x[0]
g[1] = 3.0*pow(abs(x[1]),2.0)
if x[1] < 0:
g[1] = -g[1]
return f, g
# Optimizer call
x, nf, rc = fmin_tnc(function, [-7, 3], bounds=([-10, 1], [10, 10]))
print("After", nf, "function evaluations, TNC returned:", RCSTRINGS[rc])
print("x =", x)
print("exact value = [0, 1]")
print()
example()
| 16,537 | 36.41629 | 84 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/optimize.py
|
#__docformat__ = "restructuredtext en"
# ******NOTICE***************
# optimize.py module by Travis E. Oliphant
#
# You may copy and use this module as you see fit with no
# guarantee implied provided you keep this notice in all copies.
# *****END NOTICE************
# A collection of optimization algorithms. Version 0.5
# CHANGES
# Added fminbound (July 2001)
# Added brute (Aug. 2002)
# Finished line search satisfying strong Wolfe conditions (Mar. 2004)
# Updated strong Wolfe conditions line search to use
# cubic-interpolation (Mar. 2004)
from __future__ import division, print_function, absolute_import
# Minimization routines
__all__ = ['fmin', 'fmin_powell', 'fmin_bfgs', 'fmin_ncg', 'fmin_cg',
'fminbound', 'brent', 'golden', 'bracket', 'rosen', 'rosen_der',
'rosen_hess', 'rosen_hess_prod', 'brute', 'approx_fprime',
'line_search', 'check_grad', 'OptimizeResult', 'show_options',
'OptimizeWarning']
__docformat__ = "restructuredtext en"
import warnings
import sys
import numpy
from scipy._lib.six import callable, xrange
from numpy import (atleast_1d, eye, mgrid, argmin, zeros, shape, squeeze,
vectorize, asarray, sqrt, Inf, asfarray, isinf)
import numpy as np
from .linesearch import (line_search_wolfe1, line_search_wolfe2,
line_search_wolfe2 as line_search,
LineSearchWarning)
from scipy._lib._util import getargspec_no_self as _getargspec
# standard status messages of optimizers
_status_message = {'success': 'Optimization terminated successfully.',
'maxfev': 'Maximum number of function evaluations has '
'been exceeded.',
'maxiter': 'Maximum number of iterations has been '
'exceeded.',
'pr_loss': 'Desired error not necessarily achieved due '
'to precision loss.'}
class MemoizeJac(object):
""" Decorator that caches the value gradient of function each time it
is called. """
def __init__(self, fun):
self.fun = fun
self.jac = None
self.x = None
def __call__(self, x, *args):
self.x = numpy.asarray(x).copy()
fg = self.fun(x, *args)
self.jac = fg[1]
return fg[0]
def derivative(self, x, *args):
if self.jac is not None and numpy.alltrue(x == self.x):
return self.jac
else:
self(x, *args)
return self.jac
class OptimizeResult(dict):
""" Represents the optimization result.
Attributes
----------
x : ndarray
The solution of the optimization.
success : bool
Whether or not the optimizer exited successfully.
status : int
Termination status of the optimizer. Its value depends on the
underlying solver. Refer to `message` for details.
message : str
Description of the cause of the termination.
fun, jac, hess: ndarray
Values of objective function, its Jacobian and its Hessian (if
available). The Hessians may be approximations, see the documentation
of the function in question.
hess_inv : object
Inverse of the objective function's Hessian; may be an approximation.
Not available for all solvers. The type of this attribute may be
either np.ndarray or scipy.sparse.linalg.LinearOperator.
nfev, njev, nhev : int
Number of evaluations of the objective functions and of its
Jacobian and Hessian.
nit : int
Number of iterations performed by the optimizer.
maxcv : float
The maximum constraint violation.
Notes
-----
There may be additional attributes not listed above depending of the
specific solver. Since this class is essentially a subclass of dict
with attribute accessors, one can see which attributes are available
using the `keys()` method.
"""
def __getattr__(self, name):
try:
return self[name]
except KeyError:
raise AttributeError(name)
__setattr__ = dict.__setitem__
__delattr__ = dict.__delitem__
def __repr__(self):
if self.keys():
m = max(map(len, list(self.keys()))) + 1
return '\n'.join([k.rjust(m) + ': ' + repr(v)
for k, v in sorted(self.items())])
else:
return self.__class__.__name__ + "()"
def __dir__(self):
return list(self.keys())
class OptimizeWarning(UserWarning):
pass
def _check_unknown_options(unknown_options):
if unknown_options:
msg = ", ".join(map(str, unknown_options.keys()))
# Stack level 4: this is called from _minimize_*, which is
# called from another function in Scipy. Level 4 is the first
# level in user code.
warnings.warn("Unknown solver options: %s" % msg, OptimizeWarning, 4)
def is_array_scalar(x):
"""Test whether `x` is either a scalar or an array scalar.
"""
return np.size(x) == 1
_epsilon = sqrt(numpy.finfo(float).eps)
def vecnorm(x, ord=2):
if ord == Inf:
return numpy.amax(numpy.abs(x))
elif ord == -Inf:
return numpy.amin(numpy.abs(x))
else:
return numpy.sum(numpy.abs(x)**ord, axis=0)**(1.0 / ord)
def rosen(x):
"""
The Rosenbrock function.
The function computed is::
sum(100.0*(x[1:] - x[:-1]**2.0)**2.0 + (1 - x[:-1])**2.0)
Parameters
----------
x : array_like
1-D array of points at which the Rosenbrock function is to be computed.
Returns
-------
f : float
The value of the Rosenbrock function.
See Also
--------
rosen_der, rosen_hess, rosen_hess_prod
"""
x = asarray(x)
r = numpy.sum(100.0 * (x[1:] - x[:-1]**2.0)**2.0 + (1 - x[:-1])**2.0,
axis=0)
return r
def rosen_der(x):
"""
The derivative (i.e. gradient) of the Rosenbrock function.
Parameters
----------
x : array_like
1-D array of points at which the derivative is to be computed.
Returns
-------
rosen_der : (N,) ndarray
The gradient of the Rosenbrock function at `x`.
See Also
--------
rosen, rosen_hess, rosen_hess_prod
"""
x = asarray(x)
xm = x[1:-1]
xm_m1 = x[:-2]
xm_p1 = x[2:]
der = numpy.zeros_like(x)
der[1:-1] = (200 * (xm - xm_m1**2) -
400 * (xm_p1 - xm**2) * xm - 2 * (1 - xm))
der[0] = -400 * x[0] * (x[1] - x[0]**2) - 2 * (1 - x[0])
der[-1] = 200 * (x[-1] - x[-2]**2)
return der
def rosen_hess(x):
"""
The Hessian matrix of the Rosenbrock function.
Parameters
----------
x : array_like
1-D array of points at which the Hessian matrix is to be computed.
Returns
-------
rosen_hess : ndarray
The Hessian matrix of the Rosenbrock function at `x`.
See Also
--------
rosen, rosen_der, rosen_hess_prod
"""
x = atleast_1d(x)
H = numpy.diag(-400 * x[:-1], 1) - numpy.diag(400 * x[:-1], -1)
diagonal = numpy.zeros(len(x), dtype=x.dtype)
diagonal[0] = 1200 * x[0]**2 - 400 * x[1] + 2
diagonal[-1] = 200
diagonal[1:-1] = 202 + 1200 * x[1:-1]**2 - 400 * x[2:]
H = H + numpy.diag(diagonal)
return H
def rosen_hess_prod(x, p):
"""
Product of the Hessian matrix of the Rosenbrock function with a vector.
Parameters
----------
x : array_like
1-D array of points at which the Hessian matrix is to be computed.
p : array_like
1-D array, the vector to be multiplied by the Hessian matrix.
Returns
-------
rosen_hess_prod : ndarray
The Hessian matrix of the Rosenbrock function at `x` multiplied
by the vector `p`.
See Also
--------
rosen, rosen_der, rosen_hess
"""
x = atleast_1d(x)
Hp = numpy.zeros(len(x), dtype=x.dtype)
Hp[0] = (1200 * x[0]**2 - 400 * x[1] + 2) * p[0] - 400 * x[0] * p[1]
Hp[1:-1] = (-400 * x[:-2] * p[:-2] +
(202 + 1200 * x[1:-1]**2 - 400 * x[2:]) * p[1:-1] -
400 * x[1:-1] * p[2:])
Hp[-1] = -400 * x[-2] * p[-2] + 200*p[-1]
return Hp
def wrap_function(function, args):
ncalls = [0]
if function is None:
return ncalls, None
def function_wrapper(*wrapper_args):
ncalls[0] += 1
return function(*(wrapper_args + args))
return ncalls, function_wrapper
def fmin(func, x0, args=(), xtol=1e-4, ftol=1e-4, maxiter=None, maxfun=None,
full_output=0, disp=1, retall=0, callback=None, initial_simplex=None):
"""
Minimize a function using the downhill simplex algorithm.
This algorithm only uses function values, not derivatives or second
derivatives.
Parameters
----------
func : callable func(x,*args)
The objective function to be minimized.
x0 : ndarray
Initial guess.
args : tuple, optional
Extra arguments passed to func, i.e. ``f(x,*args)``.
xtol : float, optional
Absolute error in xopt between iterations that is acceptable for
convergence.
ftol : number, optional
Absolute error in func(xopt) between iterations that is acceptable for
convergence.
maxiter : int, optional
Maximum number of iterations to perform.
maxfun : number, optional
Maximum number of function evaluations to make.
full_output : bool, optional
Set to True if fopt and warnflag outputs are desired.
disp : bool, optional
Set to True to print convergence messages.
retall : bool, optional
Set to True to return list of solutions at each iteration.
callback : callable, optional
Called after each iteration, as callback(xk), where xk is the
current parameter vector.
initial_simplex : array_like of shape (N + 1, N), optional
Initial simplex. If given, overrides `x0`.
``initial_simplex[j,:]`` should contain the coordinates of
the j-th vertex of the ``N+1`` vertices in the simplex, where
``N`` is the dimension.
Returns
-------
xopt : ndarray
Parameter that minimizes function.
fopt : float
Value of function at minimum: ``fopt = func(xopt)``.
iter : int
Number of iterations performed.
funcalls : int
Number of function calls made.
warnflag : int
1 : Maximum number of function evaluations made.
2 : Maximum number of iterations reached.
allvecs : list
Solution at each iteration.
See also
--------
minimize: Interface to minimization algorithms for multivariate
functions. See the 'Nelder-Mead' `method` in particular.
Notes
-----
Uses a Nelder-Mead simplex algorithm to find the minimum of function of
one or more variables.
This algorithm has a long history of successful use in applications.
But it will usually be slower than an algorithm that uses first or
second derivative information. In practice it can have poor
performance in high-dimensional problems and is not robust to
minimizing complicated functions. Additionally, there currently is no
complete theory describing when the algorithm will successfully
converge to the minimum, or how fast it will if it does. Both the ftol and
xtol criteria must be met for convergence.
Examples
--------
>>> def f(x):
... return x**2
>>> from scipy import optimize
>>> minimum = optimize.fmin(f, 1)
Optimization terminated successfully.
Current function value: 0.000000
Iterations: 17
Function evaluations: 34
>>> minimum[0]
-8.8817841970012523e-16
References
----------
.. [1] Nelder, J.A. and Mead, R. (1965), "A simplex method for function
minimization", The Computer Journal, 7, pp. 308-313
.. [2] Wright, M.H. (1996), "Direct Search Methods: Once Scorned, Now
Respectable", in Numerical Analysis 1995, Proceedings of the
1995 Dundee Biennial Conference in Numerical Analysis, D.F.
Griffiths and G.A. Watson (Eds.), Addison Wesley Longman,
Harlow, UK, pp. 191-208.
"""
opts = {'xatol': xtol,
'fatol': ftol,
'maxiter': maxiter,
'maxfev': maxfun,
'disp': disp,
'return_all': retall,
'initial_simplex': initial_simplex}
res = _minimize_neldermead(func, x0, args, callback=callback, **opts)
if full_output:
retlist = res['x'], res['fun'], res['nit'], res['nfev'], res['status']
if retall:
retlist += (res['allvecs'], )
return retlist
else:
if retall:
return res['x'], res['allvecs']
else:
return res['x']
def _minimize_neldermead(func, x0, args=(), callback=None,
maxiter=None, maxfev=None, disp=False,
return_all=False, initial_simplex=None,
xatol=1e-4, fatol=1e-4, adaptive=False,
**unknown_options):
"""
Minimization of scalar function of one or more variables using the
Nelder-Mead algorithm.
Options
-------
disp : bool
Set to True to print convergence messages.
maxiter, maxfev : int
Maximum allowed number of iterations and function evaluations.
Will default to ``N*200``, where ``N`` is the number of
variables, if neither `maxiter` or `maxfev` is set. If both
`maxiter` and `maxfev` are set, minimization will stop at the
first reached.
initial_simplex : array_like of shape (N + 1, N)
Initial simplex. If given, overrides `x0`.
``initial_simplex[j,:]`` should contain the coordinates of
the j-th vertex of the ``N+1`` vertices in the simplex, where
``N`` is the dimension.
xatol : float, optional
Absolute error in xopt between iterations that is acceptable for
convergence.
fatol : number, optional
Absolute error in func(xopt) between iterations that is acceptable for
convergence.
adaptive : bool, optional
Adapt algorithm parameters to dimensionality of problem. Useful for
high-dimensional minimization [1]_.
References
----------
.. [1] Gao, F. and Han, L.
Implementing the Nelder-Mead simplex algorithm with adaptive
parameters. 2012. Computational Optimization and Applications.
51:1, pp. 259-277
"""
if 'ftol' in unknown_options:
warnings.warn("ftol is deprecated for Nelder-Mead,"
" use fatol instead. If you specified both, only"
" fatol is used.",
DeprecationWarning)
if (np.isclose(fatol, 1e-4) and
not np.isclose(unknown_options['ftol'], 1e-4)):
# only ftol was probably specified, use it.
fatol = unknown_options['ftol']
unknown_options.pop('ftol')
if 'xtol' in unknown_options:
warnings.warn("xtol is deprecated for Nelder-Mead,"
" use xatol instead. If you specified both, only"
" xatol is used.",
DeprecationWarning)
if (np.isclose(xatol, 1e-4) and
not np.isclose(unknown_options['xtol'], 1e-4)):
# only xtol was probably specified, use it.
xatol = unknown_options['xtol']
unknown_options.pop('xtol')
_check_unknown_options(unknown_options)
maxfun = maxfev
retall = return_all
fcalls, func = wrap_function(func, args)
if adaptive:
dim = float(len(x0))
rho = 1
chi = 1 + 2/dim
psi = 0.75 - 1/(2*dim)
sigma = 1 - 1/dim
else:
rho = 1
chi = 2
psi = 0.5
sigma = 0.5
nonzdelt = 0.05
zdelt = 0.00025
x0 = asfarray(x0).flatten()
if initial_simplex is None:
N = len(x0)
sim = numpy.zeros((N + 1, N), dtype=x0.dtype)
sim[0] = x0
for k in range(N):
y = numpy.array(x0, copy=True)
if y[k] != 0:
y[k] = (1 + nonzdelt)*y[k]
else:
y[k] = zdelt
sim[k + 1] = y
else:
sim = np.asfarray(initial_simplex).copy()
if sim.ndim != 2 or sim.shape[0] != sim.shape[1] + 1:
raise ValueError("`initial_simplex` should be an array of shape (N+1,N)")
if len(x0) != sim.shape[1]:
raise ValueError("Size of `initial_simplex` is not consistent with `x0`")
N = sim.shape[1]
if retall:
allvecs = [sim[0]]
# If neither are set, then set both to default
if maxiter is None and maxfun is None:
maxiter = N * 200
maxfun = N * 200
elif maxiter is None:
# Convert remaining Nones, to np.inf, unless the other is np.inf, in
# which case use the default to avoid unbounded iteration
if maxfun == np.inf:
maxiter = N * 200
else:
maxiter = np.inf
elif maxfun is None:
if maxiter == np.inf:
maxfun = N * 200
else:
maxfun = np.inf
one2np1 = list(range(1, N + 1))
fsim = numpy.zeros((N + 1,), float)
for k in range(N + 1):
fsim[k] = func(sim[k])
ind = numpy.argsort(fsim)
fsim = numpy.take(fsim, ind, 0)
# sort so sim[0,:] has the lowest function value
sim = numpy.take(sim, ind, 0)
iterations = 1
while (fcalls[0] < maxfun and iterations < maxiter):
if (numpy.max(numpy.ravel(numpy.abs(sim[1:] - sim[0]))) <= xatol and
numpy.max(numpy.abs(fsim[0] - fsim[1:])) <= fatol):
break
xbar = numpy.add.reduce(sim[:-1], 0) / N
xr = (1 + rho) * xbar - rho * sim[-1]
fxr = func(xr)
doshrink = 0
if fxr < fsim[0]:
xe = (1 + rho * chi) * xbar - rho * chi * sim[-1]
fxe = func(xe)
if fxe < fxr:
sim[-1] = xe
fsim[-1] = fxe
else:
sim[-1] = xr
fsim[-1] = fxr
else: # fsim[0] <= fxr
if fxr < fsim[-2]:
sim[-1] = xr
fsim[-1] = fxr
else: # fxr >= fsim[-2]
# Perform contraction
if fxr < fsim[-1]:
xc = (1 + psi * rho) * xbar - psi * rho * sim[-1]
fxc = func(xc)
if fxc <= fxr:
sim[-1] = xc
fsim[-1] = fxc
else:
doshrink = 1
else:
# Perform an inside contraction
xcc = (1 - psi) * xbar + psi * sim[-1]
fxcc = func(xcc)
if fxcc < fsim[-1]:
sim[-1] = xcc
fsim[-1] = fxcc
else:
doshrink = 1
if doshrink:
for j in one2np1:
sim[j] = sim[0] + sigma * (sim[j] - sim[0])
fsim[j] = func(sim[j])
ind = numpy.argsort(fsim)
sim = numpy.take(sim, ind, 0)
fsim = numpy.take(fsim, ind, 0)
if callback is not None:
callback(sim[0])
iterations += 1
if retall:
allvecs.append(sim[0])
x = sim[0]
fval = numpy.min(fsim)
warnflag = 0
if fcalls[0] >= maxfun:
warnflag = 1
msg = _status_message['maxfev']
if disp:
print('Warning: ' + msg)
elif iterations >= maxiter:
warnflag = 2
msg = _status_message['maxiter']
if disp:
print('Warning: ' + msg)
else:
msg = _status_message['success']
if disp:
print(msg)
print(" Current function value: %f" % fval)
print(" Iterations: %d" % iterations)
print(" Function evaluations: %d" % fcalls[0])
result = OptimizeResult(fun=fval, nit=iterations, nfev=fcalls[0],
status=warnflag, success=(warnflag == 0),
message=msg, x=x, final_simplex=(sim, fsim))
if retall:
result['allvecs'] = allvecs
return result
def _approx_fprime_helper(xk, f, epsilon, args=(), f0=None):
"""
See ``approx_fprime``. An optional initial function value arg is added.
"""
if f0 is None:
f0 = f(*((xk,) + args))
grad = numpy.zeros((len(xk),), float)
ei = numpy.zeros((len(xk),), float)
for k in range(len(xk)):
ei[k] = 1.0
d = epsilon * ei
grad[k] = (f(*((xk + d,) + args)) - f0) / d[k]
ei[k] = 0.0
return grad
def approx_fprime(xk, f, epsilon, *args):
"""Finite-difference approximation of the gradient of a scalar function.
Parameters
----------
xk : array_like
The coordinate vector at which to determine the gradient of `f`.
f : callable
The function of which to determine the gradient (partial derivatives).
Should take `xk` as first argument, other arguments to `f` can be
supplied in ``*args``. Should return a scalar, the value of the
function at `xk`.
epsilon : array_like
Increment to `xk` to use for determining the function gradient.
If a scalar, uses the same finite difference delta for all partial
derivatives. If an array, should contain one value per element of
`xk`.
\\*args : args, optional
Any other arguments that are to be passed to `f`.
Returns
-------
grad : ndarray
The partial derivatives of `f` to `xk`.
See Also
--------
check_grad : Check correctness of gradient function against approx_fprime.
Notes
-----
The function gradient is determined by the forward finite difference
formula::
f(xk[i] + epsilon[i]) - f(xk[i])
f'[i] = ---------------------------------
epsilon[i]
The main use of `approx_fprime` is in scalar function optimizers like
`fmin_bfgs`, to determine numerically the Jacobian of a function.
Examples
--------
>>> from scipy import optimize
>>> def func(x, c0, c1):
... "Coordinate vector `x` should be an array of size two."
... return c0 * x[0]**2 + c1*x[1]**2
>>> x = np.ones(2)
>>> c0, c1 = (1, 200)
>>> eps = np.sqrt(np.finfo(float).eps)
>>> optimize.approx_fprime(x, func, [eps, np.sqrt(200) * eps], c0, c1)
array([ 2. , 400.00004198])
"""
return _approx_fprime_helper(xk, f, epsilon, args=args)
def check_grad(func, grad, x0, *args, **kwargs):
"""Check the correctness of a gradient function by comparing it against a
(forward) finite-difference approximation of the gradient.
Parameters
----------
func : callable ``func(x0, *args)``
Function whose derivative is to be checked.
grad : callable ``grad(x0, *args)``
Gradient of `func`.
x0 : ndarray
Points to check `grad` against forward difference approximation of grad
using `func`.
args : \\*args, optional
Extra arguments passed to `func` and `grad`.
epsilon : float, optional
Step size used for the finite difference approximation. It defaults to
``sqrt(numpy.finfo(float).eps)``, which is approximately 1.49e-08.
Returns
-------
err : float
The square root of the sum of squares (i.e. the 2-norm) of the
difference between ``grad(x0, *args)`` and the finite difference
approximation of `grad` using func at the points `x0`.
See Also
--------
approx_fprime
Examples
--------
>>> def func(x):
... return x[0]**2 - 0.5 * x[1]**3
>>> def grad(x):
... return [2 * x[0], -1.5 * x[1]**2]
>>> from scipy.optimize import check_grad
>>> check_grad(func, grad, [1.5, -1.5])
2.9802322387695312e-08
"""
step = kwargs.pop('epsilon', _epsilon)
if kwargs:
raise ValueError("Unknown keyword arguments: %r" %
(list(kwargs.keys()),))
return sqrt(sum((grad(x0, *args) -
approx_fprime(x0, func, step, *args))**2))
def approx_fhess_p(x0, p, fprime, epsilon, *args):
f2 = fprime(*((x0 + epsilon*p,) + args))
f1 = fprime(*((x0,) + args))
return (f2 - f1) / epsilon
class _LineSearchError(RuntimeError):
pass
def _line_search_wolfe12(f, fprime, xk, pk, gfk, old_fval, old_old_fval,
**kwargs):
"""
Same as line_search_wolfe1, but fall back to line_search_wolfe2 if
suitable step length is not found, and raise an exception if a
suitable step length is not found.
Raises
------
_LineSearchError
If no suitable step size is found
"""
extra_condition = kwargs.pop('extra_condition', None)
ret = line_search_wolfe1(f, fprime, xk, pk, gfk,
old_fval, old_old_fval,
**kwargs)
if ret[0] is not None and extra_condition is not None:
xp1 = xk + ret[0] * pk
if not extra_condition(ret[0], xp1, ret[3], ret[5]):
# Reject step if extra_condition fails
ret = (None,)
if ret[0] is None:
# line search failed: try different one.
with warnings.catch_warnings():
warnings.simplefilter('ignore', LineSearchWarning)
kwargs2 = {}
for key in ('c1', 'c2', 'amax'):
if key in kwargs:
kwargs2[key] = kwargs[key]
ret = line_search_wolfe2(f, fprime, xk, pk, gfk,
old_fval, old_old_fval,
extra_condition=extra_condition,
**kwargs2)
if ret[0] is None:
raise _LineSearchError()
return ret
def fmin_bfgs(f, x0, fprime=None, args=(), gtol=1e-5, norm=Inf,
epsilon=_epsilon, maxiter=None, full_output=0, disp=1,
retall=0, callback=None):
"""
Minimize a function using the BFGS algorithm.
Parameters
----------
f : callable f(x,*args)
Objective function to be minimized.
x0 : ndarray
Initial guess.
fprime : callable f'(x,*args), optional
Gradient of f.
args : tuple, optional
Extra arguments passed to f and fprime.
gtol : float, optional
Gradient norm must be less than gtol before successful termination.
norm : float, optional
Order of norm (Inf is max, -Inf is min)
epsilon : int or ndarray, optional
If fprime is approximated, use this value for the step size.
callback : callable, optional
An optional user-supplied function to call after each
iteration. Called as callback(xk), where xk is the
current parameter vector.
maxiter : int, optional
Maximum number of iterations to perform.
full_output : bool, optional
If True,return fopt, func_calls, grad_calls, and warnflag
in addition to xopt.
disp : bool, optional
Print convergence message if True.
retall : bool, optional
Return a list of results at each iteration if True.
Returns
-------
xopt : ndarray
Parameters which minimize f, i.e. f(xopt) == fopt.
fopt : float
Minimum value.
gopt : ndarray
Value of gradient at minimum, f'(xopt), which should be near 0.
Bopt : ndarray
Value of 1/f''(xopt), i.e. the inverse hessian matrix.
func_calls : int
Number of function_calls made.
grad_calls : int
Number of gradient calls made.
warnflag : integer
1 : Maximum number of iterations exceeded.
2 : Gradient and/or function calls not changing.
allvecs : list
The value of xopt at each iteration. Only returned if retall is True.
See also
--------
minimize: Interface to minimization algorithms for multivariate
functions. See the 'BFGS' `method` in particular.
Notes
-----
Optimize the function, f, whose gradient is given by fprime
using the quasi-Newton method of Broyden, Fletcher, Goldfarb,
and Shanno (BFGS)
References
----------
Wright, and Nocedal 'Numerical Optimization', 1999, pg. 198.
"""
opts = {'gtol': gtol,
'norm': norm,
'eps': epsilon,
'disp': disp,
'maxiter': maxiter,
'return_all': retall}
res = _minimize_bfgs(f, x0, args, fprime, callback=callback, **opts)
if full_output:
retlist = (res['x'], res['fun'], res['jac'], res['hess_inv'],
res['nfev'], res['njev'], res['status'])
if retall:
retlist += (res['allvecs'], )
return retlist
else:
if retall:
return res['x'], res['allvecs']
else:
return res['x']
def _minimize_bfgs(fun, x0, args=(), jac=None, callback=None,
gtol=1e-5, norm=Inf, eps=_epsilon, maxiter=None,
disp=False, return_all=False,
**unknown_options):
"""
Minimization of scalar function of one or more variables using the
BFGS algorithm.
Options
-------
disp : bool
Set to True to print convergence messages.
maxiter : int
Maximum number of iterations to perform.
gtol : float
Gradient norm must be less than `gtol` before successful
termination.
norm : float
Order of norm (Inf is max, -Inf is min).
eps : float or ndarray
If `jac` is approximated, use this value for the step size.
"""
_check_unknown_options(unknown_options)
f = fun
fprime = jac
epsilon = eps
retall = return_all
x0 = asarray(x0).flatten()
if x0.ndim == 0:
x0.shape = (1,)
if maxiter is None:
maxiter = len(x0) * 200
func_calls, f = wrap_function(f, args)
if fprime is None:
grad_calls, myfprime = wrap_function(approx_fprime, (f, epsilon))
else:
grad_calls, myfprime = wrap_function(fprime, args)
gfk = myfprime(x0)
k = 0
N = len(x0)
I = numpy.eye(N, dtype=int)
Hk = I
# Sets the initial step guess to dx ~ 1
old_fval = f(x0)
old_old_fval = old_fval + np.linalg.norm(gfk) / 2
xk = x0
if retall:
allvecs = [x0]
warnflag = 0
gnorm = vecnorm(gfk, ord=norm)
while (gnorm > gtol) and (k < maxiter):
pk = -numpy.dot(Hk, gfk)
try:
alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = \
_line_search_wolfe12(f, myfprime, xk, pk, gfk,
old_fval, old_old_fval, amin=1e-100, amax=1e100)
except _LineSearchError:
# Line search failed to find a better solution.
warnflag = 2
break
xkp1 = xk + alpha_k * pk
if retall:
allvecs.append(xkp1)
sk = xkp1 - xk
xk = xkp1
if gfkp1 is None:
gfkp1 = myfprime(xkp1)
yk = gfkp1 - gfk
gfk = gfkp1
if callback is not None:
callback(xk)
k += 1
gnorm = vecnorm(gfk, ord=norm)
if (gnorm <= gtol):
break
if not numpy.isfinite(old_fval):
# We correctly found +-Inf as optimal value, or something went
# wrong.
warnflag = 2
break
try: # this was handled in numeric, let it remaines for more safety
rhok = 1.0 / (numpy.dot(yk, sk))
except ZeroDivisionError:
rhok = 1000.0
if disp:
print("Divide-by-zero encountered: rhok assumed large")
if isinf(rhok): # this is patch for numpy
rhok = 1000.0
if disp:
print("Divide-by-zero encountered: rhok assumed large")
A1 = I - sk[:, numpy.newaxis] * yk[numpy.newaxis, :] * rhok
A2 = I - yk[:, numpy.newaxis] * sk[numpy.newaxis, :] * rhok
Hk = numpy.dot(A1, numpy.dot(Hk, A2)) + (rhok * sk[:, numpy.newaxis] *
sk[numpy.newaxis, :])
fval = old_fval
if np.isnan(fval):
# This can happen if the first call to f returned NaN;
# the loop is then never entered.
warnflag = 2
if warnflag == 2:
msg = _status_message['pr_loss']
elif k >= maxiter:
warnflag = 1
msg = _status_message['maxiter']
else:
msg = _status_message['success']
if disp:
print("%s%s" % ("Warning: " if warnflag != 0 else "", msg))
print(" Current function value: %f" % fval)
print(" Iterations: %d" % k)
print(" Function evaluations: %d" % func_calls[0])
print(" Gradient evaluations: %d" % grad_calls[0])
result = OptimizeResult(fun=fval, jac=gfk, hess_inv=Hk, nfev=func_calls[0],
njev=grad_calls[0], status=warnflag,
success=(warnflag == 0), message=msg, x=xk,
nit=k)
if retall:
result['allvecs'] = allvecs
return result
def fmin_cg(f, x0, fprime=None, args=(), gtol=1e-5, norm=Inf, epsilon=_epsilon,
maxiter=None, full_output=0, disp=1, retall=0, callback=None):
"""
Minimize a function using a nonlinear conjugate gradient algorithm.
Parameters
----------
f : callable, ``f(x, *args)``
Objective function to be minimized. Here `x` must be a 1-D array of
the variables that are to be changed in the search for a minimum, and
`args` are the other (fixed) parameters of `f`.
x0 : ndarray
A user-supplied initial estimate of `xopt`, the optimal value of `x`.
It must be a 1-D array of values.
fprime : callable, ``fprime(x, *args)``, optional
A function that returns the gradient of `f` at `x`. Here `x` and `args`
are as described above for `f`. The returned value must be a 1-D array.
Defaults to None, in which case the gradient is approximated
numerically (see `epsilon`, below).
args : tuple, optional
Parameter values passed to `f` and `fprime`. Must be supplied whenever
additional fixed parameters are needed to completely specify the
functions `f` and `fprime`.
gtol : float, optional
Stop when the norm of the gradient is less than `gtol`.
norm : float, optional
Order to use for the norm of the gradient
(``-np.Inf`` is min, ``np.Inf`` is max).
epsilon : float or ndarray, optional
Step size(s) to use when `fprime` is approximated numerically. Can be a
scalar or a 1-D array. Defaults to ``sqrt(eps)``, with eps the
floating point machine precision. Usually ``sqrt(eps)`` is about
1.5e-8.
maxiter : int, optional
Maximum number of iterations to perform. Default is ``200 * len(x0)``.
full_output : bool, optional
If True, return `fopt`, `func_calls`, `grad_calls`, and `warnflag` in
addition to `xopt`. See the Returns section below for additional
information on optional return values.
disp : bool, optional
If True, return a convergence message, followed by `xopt`.
retall : bool, optional
If True, add to the returned values the results of each iteration.
callback : callable, optional
An optional user-supplied function, called after each iteration.
Called as ``callback(xk)``, where ``xk`` is the current value of `x0`.
Returns
-------
xopt : ndarray
Parameters which minimize f, i.e. ``f(xopt) == fopt``.
fopt : float, optional
Minimum value found, f(xopt). Only returned if `full_output` is True.
func_calls : int, optional
The number of function_calls made. Only returned if `full_output`
is True.
grad_calls : int, optional
The number of gradient calls made. Only returned if `full_output` is
True.
warnflag : int, optional
Integer value with warning status, only returned if `full_output` is
True.
0 : Success.
1 : The maximum number of iterations was exceeded.
2 : Gradient and/or function calls were not changing. May indicate
that precision was lost, i.e., the routine did not converge.
allvecs : list of ndarray, optional
List of arrays, containing the results at each iteration.
Only returned if `retall` is True.
See Also
--------
minimize : common interface to all `scipy.optimize` algorithms for
unconstrained and constrained minimization of multivariate
functions. It provides an alternative way to call
``fmin_cg``, by specifying ``method='CG'``.
Notes
-----
This conjugate gradient algorithm is based on that of Polak and Ribiere
[1]_.
Conjugate gradient methods tend to work better when:
1. `f` has a unique global minimizing point, and no local minima or
other stationary points,
2. `f` is, at least locally, reasonably well approximated by a
quadratic function of the variables,
3. `f` is continuous and has a continuous gradient,
4. `fprime` is not too large, e.g., has a norm less than 1000,
5. The initial guess, `x0`, is reasonably close to `f` 's global
minimizing point, `xopt`.
References
----------
.. [1] Wright & Nocedal, "Numerical Optimization", 1999, pp. 120-122.
Examples
--------
Example 1: seek the minimum value of the expression
``a*u**2 + b*u*v + c*v**2 + d*u + e*v + f`` for given values
of the parameters and an initial guess ``(u, v) = (0, 0)``.
>>> args = (2, 3, 7, 8, 9, 10) # parameter values
>>> def f(x, *args):
... u, v = x
... a, b, c, d, e, f = args
... return a*u**2 + b*u*v + c*v**2 + d*u + e*v + f
>>> def gradf(x, *args):
... u, v = x
... a, b, c, d, e, f = args
... gu = 2*a*u + b*v + d # u-component of the gradient
... gv = b*u + 2*c*v + e # v-component of the gradient
... return np.asarray((gu, gv))
>>> x0 = np.asarray((0, 0)) # Initial guess.
>>> from scipy import optimize
>>> res1 = optimize.fmin_cg(f, x0, fprime=gradf, args=args)
Optimization terminated successfully.
Current function value: 1.617021
Iterations: 4
Function evaluations: 8
Gradient evaluations: 8
>>> res1
array([-1.80851064, -0.25531915])
Example 2: solve the same problem using the `minimize` function.
(This `myopts` dictionary shows all of the available options,
although in practice only non-default values would be needed.
The returned value will be a dictionary.)
>>> opts = {'maxiter' : None, # default value.
... 'disp' : True, # non-default value.
... 'gtol' : 1e-5, # default value.
... 'norm' : np.inf, # default value.
... 'eps' : 1.4901161193847656e-08} # default value.
>>> res2 = optimize.minimize(f, x0, jac=gradf, args=args,
... method='CG', options=opts)
Optimization terminated successfully.
Current function value: 1.617021
Iterations: 4
Function evaluations: 8
Gradient evaluations: 8
>>> res2.x # minimum found
array([-1.80851064, -0.25531915])
"""
opts = {'gtol': gtol,
'norm': norm,
'eps': epsilon,
'disp': disp,
'maxiter': maxiter,
'return_all': retall}
res = _minimize_cg(f, x0, args, fprime, callback=callback, **opts)
if full_output:
retlist = res['x'], res['fun'], res['nfev'], res['njev'], res['status']
if retall:
retlist += (res['allvecs'], )
return retlist
else:
if retall:
return res['x'], res['allvecs']
else:
return res['x']
def _minimize_cg(fun, x0, args=(), jac=None, callback=None,
gtol=1e-5, norm=Inf, eps=_epsilon, maxiter=None,
disp=False, return_all=False,
**unknown_options):
"""
Minimization of scalar function of one or more variables using the
conjugate gradient algorithm.
Options
-------
disp : bool
Set to True to print convergence messages.
maxiter : int
Maximum number of iterations to perform.
gtol : float
Gradient norm must be less than `gtol` before successful
termination.
norm : float
Order of norm (Inf is max, -Inf is min).
eps : float or ndarray
If `jac` is approximated, use this value for the step size.
"""
_check_unknown_options(unknown_options)
f = fun
fprime = jac
epsilon = eps
retall = return_all
x0 = asarray(x0).flatten()
if maxiter is None:
maxiter = len(x0) * 200
func_calls, f = wrap_function(f, args)
if fprime is None:
grad_calls, myfprime = wrap_function(approx_fprime, (f, epsilon))
else:
grad_calls, myfprime = wrap_function(fprime, args)
gfk = myfprime(x0)
k = 0
xk = x0
# Sets the initial step guess to dx ~ 1
old_fval = f(xk)
old_old_fval = old_fval + np.linalg.norm(gfk) / 2
if retall:
allvecs = [xk]
warnflag = 0
pk = -gfk
gnorm = vecnorm(gfk, ord=norm)
sigma_3 = 0.01
while (gnorm > gtol) and (k < maxiter):
deltak = numpy.dot(gfk, gfk)
cached_step = [None]
def polak_ribiere_powell_step(alpha, gfkp1=None):
xkp1 = xk + alpha * pk
if gfkp1 is None:
gfkp1 = myfprime(xkp1)
yk = gfkp1 - gfk
beta_k = max(0, numpy.dot(yk, gfkp1) / deltak)
pkp1 = -gfkp1 + beta_k * pk
gnorm = vecnorm(gfkp1, ord=norm)
return (alpha, xkp1, pkp1, gfkp1, gnorm)
def descent_condition(alpha, xkp1, fp1, gfkp1):
# Polak-Ribiere+ needs an explicit check of a sufficient
# descent condition, which is not guaranteed by strong Wolfe.
#
# See Gilbert & Nocedal, "Global convergence properties of
# conjugate gradient methods for optimization",
# SIAM J. Optimization 2, 21 (1992).
cached_step[:] = polak_ribiere_powell_step(alpha, gfkp1)
alpha, xk, pk, gfk, gnorm = cached_step
# Accept step if it leads to convergence.
if gnorm <= gtol:
return True
# Accept step if sufficient descent condition applies.
return numpy.dot(pk, gfk) <= -sigma_3 * numpy.dot(gfk, gfk)
try:
alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = \
_line_search_wolfe12(f, myfprime, xk, pk, gfk, old_fval,
old_old_fval, c2=0.4, amin=1e-100, amax=1e100,
extra_condition=descent_condition)
except _LineSearchError:
# Line search failed to find a better solution.
warnflag = 2
break
# Reuse already computed results if possible
if alpha_k == cached_step[0]:
alpha_k, xk, pk, gfk, gnorm = cached_step
else:
alpha_k, xk, pk, gfk, gnorm = polak_ribiere_powell_step(alpha_k, gfkp1)
if retall:
allvecs.append(xk)
if callback is not None:
callback(xk)
k += 1
fval = old_fval
if warnflag == 2:
msg = _status_message['pr_loss']
elif k >= maxiter:
warnflag = 1
msg = _status_message['maxiter']
else:
msg = _status_message['success']
if disp:
print("%s%s" % ("Warning: " if warnflag != 0 else "", msg))
print(" Current function value: %f" % fval)
print(" Iterations: %d" % k)
print(" Function evaluations: %d" % func_calls[0])
print(" Gradient evaluations: %d" % grad_calls[0])
result = OptimizeResult(fun=fval, jac=gfk, nfev=func_calls[0],
njev=grad_calls[0], status=warnflag,
success=(warnflag == 0), message=msg, x=xk,
nit=k)
if retall:
result['allvecs'] = allvecs
return result
def fmin_ncg(f, x0, fprime, fhess_p=None, fhess=None, args=(), avextol=1e-5,
epsilon=_epsilon, maxiter=None, full_output=0, disp=1, retall=0,
callback=None):
"""
Unconstrained minimization of a function using the Newton-CG method.
Parameters
----------
f : callable ``f(x, *args)``
Objective function to be minimized.
x0 : ndarray
Initial guess.
fprime : callable ``f'(x, *args)``
Gradient of f.
fhess_p : callable ``fhess_p(x, p, *args)``, optional
Function which computes the Hessian of f times an
arbitrary vector, p.
fhess : callable ``fhess(x, *args)``, optional
Function to compute the Hessian matrix of f.
args : tuple, optional
Extra arguments passed to f, fprime, fhess_p, and fhess
(the same set of extra arguments is supplied to all of
these functions).
epsilon : float or ndarray, optional
If fhess is approximated, use this value for the step size.
callback : callable, optional
An optional user-supplied function which is called after
each iteration. Called as callback(xk), where xk is the
current parameter vector.
avextol : float, optional
Convergence is assumed when the average relative error in
the minimizer falls below this amount.
maxiter : int, optional
Maximum number of iterations to perform.
full_output : bool, optional
If True, return the optional outputs.
disp : bool, optional
If True, print convergence message.
retall : bool, optional
If True, return a list of results at each iteration.
Returns
-------
xopt : ndarray
Parameters which minimize f, i.e. ``f(xopt) == fopt``.
fopt : float
Value of the function at xopt, i.e. ``fopt = f(xopt)``.
fcalls : int
Number of function calls made.
gcalls : int
Number of gradient calls made.
hcalls : int
Number of hessian calls made.
warnflag : int
Warnings generated by the algorithm.
1 : Maximum number of iterations exceeded.
allvecs : list
The result at each iteration, if retall is True (see below).
See also
--------
minimize: Interface to minimization algorithms for multivariate
functions. See the 'Newton-CG' `method` in particular.
Notes
-----
Only one of `fhess_p` or `fhess` need to be given. If `fhess`
is provided, then `fhess_p` will be ignored. If neither `fhess`
nor `fhess_p` is provided, then the hessian product will be
approximated using finite differences on `fprime`. `fhess_p`
must compute the hessian times an arbitrary vector. If it is not
given, finite-differences on `fprime` are used to compute
it.
Newton-CG methods are also called truncated Newton methods. This
function differs from scipy.optimize.fmin_tnc because
1. scipy.optimize.fmin_ncg is written purely in python using numpy
and scipy while scipy.optimize.fmin_tnc calls a C function.
2. scipy.optimize.fmin_ncg is only for unconstrained minimization
while scipy.optimize.fmin_tnc is for unconstrained minimization
or box constrained minimization. (Box constraints give
lower and upper bounds for each variable separately.)
References
----------
Wright & Nocedal, 'Numerical Optimization', 1999, pg. 140.
"""
opts = {'xtol': avextol,
'eps': epsilon,
'maxiter': maxiter,
'disp': disp,
'return_all': retall}
res = _minimize_newtoncg(f, x0, args, fprime, fhess, fhess_p,
callback=callback, **opts)
if full_output:
retlist = (res['x'], res['fun'], res['nfev'], res['njev'],
res['nhev'], res['status'])
if retall:
retlist += (res['allvecs'], )
return retlist
else:
if retall:
return res['x'], res['allvecs']
else:
return res['x']
def _minimize_newtoncg(fun, x0, args=(), jac=None, hess=None, hessp=None,
callback=None, xtol=1e-5, eps=_epsilon, maxiter=None,
disp=False, return_all=False,
**unknown_options):
"""
Minimization of scalar function of one or more variables using the
Newton-CG algorithm.
Note that the `jac` parameter (Jacobian) is required.
Options
-------
disp : bool
Set to True to print convergence messages.
xtol : float
Average relative error in solution `xopt` acceptable for
convergence.
maxiter : int
Maximum number of iterations to perform.
eps : float or ndarray
If `jac` is approximated, use this value for the step size.
"""
_check_unknown_options(unknown_options)
if jac is None:
raise ValueError('Jacobian is required for Newton-CG method')
f = fun
fprime = jac
fhess_p = hessp
fhess = hess
avextol = xtol
epsilon = eps
retall = return_all
def terminate(warnflag, msg):
if disp:
print(msg)
print(" Current function value: %f" % old_fval)
print(" Iterations: %d" % k)
print(" Function evaluations: %d" % fcalls[0])
print(" Gradient evaluations: %d" % gcalls[0])
print(" Hessian evaluations: %d" % hcalls)
fval = old_fval
result = OptimizeResult(fun=fval, jac=gfk, nfev=fcalls[0],
njev=gcalls[0], nhev=hcalls, status=warnflag,
success=(warnflag == 0), message=msg, x=xk,
nit=k)
if retall:
result['allvecs'] = allvecs
return result
x0 = asarray(x0).flatten()
fcalls, f = wrap_function(f, args)
gcalls, fprime = wrap_function(fprime, args)
hcalls = 0
if maxiter is None:
maxiter = len(x0)*200
cg_maxiter = 20*len(x0)
xtol = len(x0) * avextol
update = [2 * xtol]
xk = x0
if retall:
allvecs = [xk]
k = 0
gfk = None
old_fval = f(x0)
old_old_fval = None
float64eps = numpy.finfo(numpy.float64).eps
while numpy.add.reduce(numpy.abs(update)) > xtol:
if k >= maxiter:
msg = "Warning: " + _status_message['maxiter']
return terminate(1, msg)
# Compute a search direction pk by applying the CG method to
# del2 f(xk) p = - grad f(xk) starting from 0.
b = -fprime(xk)
maggrad = numpy.add.reduce(numpy.abs(b))
eta = numpy.min([0.5, numpy.sqrt(maggrad)])
termcond = eta * maggrad
xsupi = zeros(len(x0), dtype=x0.dtype)
ri = -b
psupi = -ri
i = 0
dri0 = numpy.dot(ri, ri)
if fhess is not None: # you want to compute hessian once.
A = fhess(*(xk,) + args)
hcalls = hcalls + 1
for k2 in xrange(cg_maxiter):
if numpy.add.reduce(numpy.abs(ri)) <= termcond:
break
if fhess is None:
if fhess_p is None:
Ap = approx_fhess_p(xk, psupi, fprime, epsilon)
else:
Ap = fhess_p(xk, psupi, *args)
hcalls = hcalls + 1
else:
Ap = numpy.dot(A, psupi)
# check curvature
Ap = asarray(Ap).squeeze() # get rid of matrices...
curv = numpy.dot(psupi, Ap)
if 0 <= curv <= 3 * float64eps:
break
elif curv < 0:
if (i > 0):
break
else:
# fall back to steepest descent direction
xsupi = dri0 / (-curv) * b
break
alphai = dri0 / curv
xsupi = xsupi + alphai * psupi
ri = ri + alphai * Ap
dri1 = numpy.dot(ri, ri)
betai = dri1 / dri0
psupi = -ri + betai * psupi
i = i + 1
dri0 = dri1 # update numpy.dot(ri,ri) for next time.
else:
# curvature keeps increasing, bail out
msg = ("Warning: CG iterations didn't converge. The Hessian is not "
"positive definite.")
return terminate(3, msg)
pk = xsupi # search direction is solution to system.
gfk = -b # gradient at xk
try:
alphak, fc, gc, old_fval, old_old_fval, gfkp1 = \
_line_search_wolfe12(f, fprime, xk, pk, gfk,
old_fval, old_old_fval)
except _LineSearchError:
# Line search failed to find a better solution.
msg = "Warning: " + _status_message['pr_loss']
return terminate(2, msg)
update = alphak * pk
xk = xk + update # upcast if necessary
if callback is not None:
callback(xk)
if retall:
allvecs.append(xk)
k += 1
else:
msg = _status_message['success']
return terminate(0, msg)
def fminbound(func, x1, x2, args=(), xtol=1e-5, maxfun=500,
full_output=0, disp=1):
"""Bounded minimization for scalar functions.
Parameters
----------
func : callable f(x,*args)
Objective function to be minimized (must accept and return scalars).
x1, x2 : float or array scalar
The optimization bounds.
args : tuple, optional
Extra arguments passed to function.
xtol : float, optional
The convergence tolerance.
maxfun : int, optional
Maximum number of function evaluations allowed.
full_output : bool, optional
If True, return optional outputs.
disp : int, optional
If non-zero, print messages.
0 : no message printing.
1 : non-convergence notification messages only.
2 : print a message on convergence too.
3 : print iteration results.
Returns
-------
xopt : ndarray
Parameters (over given interval) which minimize the
objective function.
fval : number
The function value at the minimum point.
ierr : int
An error flag (0 if converged, 1 if maximum number of
function calls reached).
numfunc : int
The number of function calls made.
See also
--------
minimize_scalar: Interface to minimization algorithms for scalar
univariate functions. See the 'Bounded' `method` in particular.
Notes
-----
Finds a local minimizer of the scalar function `func` in the
interval x1 < xopt < x2 using Brent's method. (See `brent`
for auto-bracketing).
Examples
--------
`fminbound` finds the minimum of the function in the given range.
The following examples illustrate the same
>>> def f(x):
... return x**2
>>> from scipy import optimize
>>> minimum = optimize.fminbound(f, -1, 2)
>>> minimum
0.0
>>> minimum = optimize.fminbound(f, 1, 2)
>>> minimum
1.0000059608609866
"""
options = {'xatol': xtol,
'maxiter': maxfun,
'disp': disp}
res = _minimize_scalar_bounded(func, (x1, x2), args, **options)
if full_output:
return res['x'], res['fun'], res['status'], res['nfev']
else:
return res['x']
def _minimize_scalar_bounded(func, bounds, args=(),
xatol=1e-5, maxiter=500, disp=0,
**unknown_options):
"""
Options
-------
maxiter : int
Maximum number of iterations to perform.
disp: int, optional
If non-zero, print messages.
0 : no message printing.
1 : non-convergence notification messages only.
2 : print a message on convergence too.
3 : print iteration results.
xatol : float
Absolute error in solution `xopt` acceptable for convergence.
"""
_check_unknown_options(unknown_options)
maxfun = maxiter
# Test bounds are of correct form
if len(bounds) != 2:
raise ValueError('bounds must have two elements.')
x1, x2 = bounds
if not (is_array_scalar(x1) and is_array_scalar(x2)):
raise ValueError("Optimisation bounds must be scalars"
" or array scalars.")
if x1 > x2:
raise ValueError("The lower bound exceeds the upper bound.")
flag = 0
header = ' Func-count x f(x) Procedure'
step = ' initial'
sqrt_eps = sqrt(2.2e-16)
golden_mean = 0.5 * (3.0 - sqrt(5.0))
a, b = x1, x2
fulc = a + golden_mean * (b - a)
nfc, xf = fulc, fulc
rat = e = 0.0
x = xf
fx = func(x, *args)
num = 1
fmin_data = (1, xf, fx)
ffulc = fnfc = fx
xm = 0.5 * (a + b)
tol1 = sqrt_eps * numpy.abs(xf) + xatol / 3.0
tol2 = 2.0 * tol1
if disp > 2:
print(" ")
print(header)
print("%5.0f %12.6g %12.6g %s" % (fmin_data + (step,)))
while (numpy.abs(xf - xm) > (tol2 - 0.5 * (b - a))):
golden = 1
# Check for parabolic fit
if numpy.abs(e) > tol1:
golden = 0
r = (xf - nfc) * (fx - ffulc)
q = (xf - fulc) * (fx - fnfc)
p = (xf - fulc) * q - (xf - nfc) * r
q = 2.0 * (q - r)
if q > 0.0:
p = -p
q = numpy.abs(q)
r = e
e = rat
# Check for acceptability of parabola
if ((numpy.abs(p) < numpy.abs(0.5*q*r)) and (p > q*(a - xf)) and
(p < q * (b - xf))):
rat = (p + 0.0) / q
x = xf + rat
step = ' parabolic'
if ((x - a) < tol2) or ((b - x) < tol2):
si = numpy.sign(xm - xf) + ((xm - xf) == 0)
rat = tol1 * si
else: # do a golden section step
golden = 1
if golden: # Do a golden-section step
if xf >= xm:
e = a - xf
else:
e = b - xf
rat = golden_mean*e
step = ' golden'
si = numpy.sign(rat) + (rat == 0)
x = xf + si * numpy.max([numpy.abs(rat), tol1])
fu = func(x, *args)
num += 1
fmin_data = (num, x, fu)
if disp > 2:
print("%5.0f %12.6g %12.6g %s" % (fmin_data + (step,)))
if fu <= fx:
if x >= xf:
a = xf
else:
b = xf
fulc, ffulc = nfc, fnfc
nfc, fnfc = xf, fx
xf, fx = x, fu
else:
if x < xf:
a = x
else:
b = x
if (fu <= fnfc) or (nfc == xf):
fulc, ffulc = nfc, fnfc
nfc, fnfc = x, fu
elif (fu <= ffulc) or (fulc == xf) or (fulc == nfc):
fulc, ffulc = x, fu
xm = 0.5 * (a + b)
tol1 = sqrt_eps * numpy.abs(xf) + xatol / 3.0
tol2 = 2.0 * tol1
if num >= maxfun:
flag = 1
break
fval = fx
if disp > 0:
_endprint(x, flag, fval, maxfun, xatol, disp)
result = OptimizeResult(fun=fval, status=flag, success=(flag == 0),
message={0: 'Solution found.',
1: 'Maximum number of function calls '
'reached.'}.get(flag, ''),
x=xf, nfev=num)
return result
class Brent:
#need to rethink design of __init__
def __init__(self, func, args=(), tol=1.48e-8, maxiter=500,
full_output=0):
self.func = func
self.args = args
self.tol = tol
self.maxiter = maxiter
self._mintol = 1.0e-11
self._cg = 0.3819660
self.xmin = None
self.fval = None
self.iter = 0
self.funcalls = 0
# need to rethink design of set_bracket (new options, etc)
def set_bracket(self, brack=None):
self.brack = brack
def get_bracket_info(self):
#set up
func = self.func
args = self.args
brack = self.brack
### BEGIN core bracket_info code ###
### carefully DOCUMENT any CHANGES in core ##
if brack is None:
xa, xb, xc, fa, fb, fc, funcalls = bracket(func, args=args)
elif len(brack) == 2:
xa, xb, xc, fa, fb, fc, funcalls = bracket(func, xa=brack[0],
xb=brack[1], args=args)
elif len(brack) == 3:
xa, xb, xc = brack
if (xa > xc): # swap so xa < xc can be assumed
xc, xa = xa, xc
if not ((xa < xb) and (xb < xc)):
raise ValueError("Not a bracketing interval.")
fa = func(*((xa,) + args))
fb = func(*((xb,) + args))
fc = func(*((xc,) + args))
if not ((fb < fa) and (fb < fc)):
raise ValueError("Not a bracketing interval.")
funcalls = 3
else:
raise ValueError("Bracketing interval must be "
"length 2 or 3 sequence.")
### END core bracket_info code ###
return xa, xb, xc, fa, fb, fc, funcalls
def optimize(self):
# set up for optimization
func = self.func
xa, xb, xc, fa, fb, fc, funcalls = self.get_bracket_info()
_mintol = self._mintol
_cg = self._cg
#################################
#BEGIN CORE ALGORITHM
#################################
x = w = v = xb
fw = fv = fx = func(*((x,) + self.args))
if (xa < xc):
a = xa
b = xc
else:
a = xc
b = xa
deltax = 0.0
funcalls += 1
iter = 0
while (iter < self.maxiter):
tol1 = self.tol * numpy.abs(x) + _mintol
tol2 = 2.0 * tol1
xmid = 0.5 * (a + b)
# check for convergence
if numpy.abs(x - xmid) < (tol2 - 0.5 * (b - a)):
break
# XXX In the first iteration, rat is only bound in the true case
# of this conditional. This used to cause an UnboundLocalError
# (gh-4140). It should be set before the if (but to what?).
if (numpy.abs(deltax) <= tol1):
if (x >= xmid):
deltax = a - x # do a golden section step
else:
deltax = b - x
rat = _cg * deltax
else: # do a parabolic step
tmp1 = (x - w) * (fx - fv)
tmp2 = (x - v) * (fx - fw)
p = (x - v) * tmp2 - (x - w) * tmp1
tmp2 = 2.0 * (tmp2 - tmp1)
if (tmp2 > 0.0):
p = -p
tmp2 = numpy.abs(tmp2)
dx_temp = deltax
deltax = rat
# check parabolic fit
if ((p > tmp2 * (a - x)) and (p < tmp2 * (b - x)) and
(numpy.abs(p) < numpy.abs(0.5 * tmp2 * dx_temp))):
rat = p * 1.0 / tmp2 # if parabolic step is useful.
u = x + rat
if ((u - a) < tol2 or (b - u) < tol2):
if xmid - x >= 0:
rat = tol1
else:
rat = -tol1
else:
if (x >= xmid):
deltax = a - x # if it's not do a golden section step
else:
deltax = b - x
rat = _cg * deltax
if (numpy.abs(rat) < tol1): # update by at least tol1
if rat >= 0:
u = x + tol1
else:
u = x - tol1
else:
u = x + rat
fu = func(*((u,) + self.args)) # calculate new output value
funcalls += 1
if (fu > fx): # if it's bigger than current
if (u < x):
a = u
else:
b = u
if (fu <= fw) or (w == x):
v = w
w = u
fv = fw
fw = fu
elif (fu <= fv) or (v == x) or (v == w):
v = u
fv = fu
else:
if (u >= x):
a = x
else:
b = x
v = w
w = x
x = u
fv = fw
fw = fx
fx = fu
iter += 1
#################################
#END CORE ALGORITHM
#################################
self.xmin = x
self.fval = fx
self.iter = iter
self.funcalls = funcalls
def get_result(self, full_output=False):
if full_output:
return self.xmin, self.fval, self.iter, self.funcalls
else:
return self.xmin
def brent(func, args=(), brack=None, tol=1.48e-8, full_output=0, maxiter=500):
"""
Given a function of one-variable and a possible bracket, return
the local minimum of the function isolated to a fractional precision
of tol.
Parameters
----------
func : callable f(x,*args)
Objective function.
args : tuple, optional
Additional arguments (if present).
brack : tuple, optional
Either a triple (xa,xb,xc) where xa<xb<xc and func(xb) <
func(xa), func(xc) or a pair (xa,xb) which are used as a
starting interval for a downhill bracket search (see
`bracket`). Providing the pair (xa,xb) does not always mean
the obtained solution will satisfy xa<=x<=xb.
tol : float, optional
Stop if between iteration change is less than `tol`.
full_output : bool, optional
If True, return all output args (xmin, fval, iter,
funcalls).
maxiter : int, optional
Maximum number of iterations in solution.
Returns
-------
xmin : ndarray
Optimum point.
fval : float
Optimum value.
iter : int
Number of iterations.
funcalls : int
Number of objective function evaluations made.
See also
--------
minimize_scalar: Interface to minimization algorithms for scalar
univariate functions. See the 'Brent' `method` in particular.
Notes
-----
Uses inverse parabolic interpolation when possible to speed up
convergence of golden section method.
Does not ensure that the minimum lies in the range specified by
`brack`. See `fminbound`.
Examples
--------
We illustrate the behaviour of the function when `brack` is of
size 2 and 3 respectively. In the case where `brack` is of the
form (xa,xb), we can see for the given values, the output need
not necessarily lie in the range (xa,xb).
>>> def f(x):
... return x**2
>>> from scipy import optimize
>>> minimum = optimize.brent(f,brack=(1,2))
>>> minimum
0.0
>>> minimum = optimize.brent(f,brack=(-1,0.5,2))
>>> minimum
-2.7755575615628914e-17
"""
options = {'xtol': tol,
'maxiter': maxiter}
res = _minimize_scalar_brent(func, brack, args, **options)
if full_output:
return res['x'], res['fun'], res['nit'], res['nfev']
else:
return res['x']
def _minimize_scalar_brent(func, brack=None, args=(),
xtol=1.48e-8, maxiter=500,
**unknown_options):
"""
Options
-------
maxiter : int
Maximum number of iterations to perform.
xtol : float
Relative error in solution `xopt` acceptable for convergence.
Notes
-----
Uses inverse parabolic interpolation when possible to speed up
convergence of golden section method.
"""
_check_unknown_options(unknown_options)
tol = xtol
if tol < 0:
raise ValueError('tolerance should be >= 0, got %r' % tol)
brent = Brent(func=func, args=args, tol=tol,
full_output=True, maxiter=maxiter)
brent.set_bracket(brack)
brent.optimize()
x, fval, nit, nfev = brent.get_result(full_output=True)
return OptimizeResult(fun=fval, x=x, nit=nit, nfev=nfev,
success=nit < maxiter)
def golden(func, args=(), brack=None, tol=_epsilon,
full_output=0, maxiter=5000):
"""
Return the minimum of a function of one variable using golden section
method.
Given a function of one variable and a possible bracketing interval,
return the minimum of the function isolated to a fractional precision of
tol.
Parameters
----------
func : callable func(x,*args)
Objective function to minimize.
args : tuple, optional
Additional arguments (if present), passed to func.
brack : tuple, optional
Triple (a,b,c), where (a<b<c) and func(b) <
func(a),func(c). If bracket consists of two numbers (a,
c), then they are assumed to be a starting interval for a
downhill bracket search (see `bracket`); it doesn't always
mean that obtained solution will satisfy a<=x<=c.
tol : float, optional
x tolerance stop criterion
full_output : bool, optional
If True, return optional outputs.
maxiter : int
Maximum number of iterations to perform.
See also
--------
minimize_scalar: Interface to minimization algorithms for scalar
univariate functions. See the 'Golden' `method` in particular.
Notes
-----
Uses analog of bisection method to decrease the bracketed
interval.
Examples
--------
We illustrate the behaviour of the function when `brack` is of
size 2 and 3 respectively. In the case where `brack` is of the
form (xa,xb), we can see for the given values, the output need
not necessarily lie in the range ``(xa, xb)``.
>>> def f(x):
... return x**2
>>> from scipy import optimize
>>> minimum = optimize.golden(f, brack=(1, 2))
>>> minimum
1.5717277788484873e-162
>>> minimum = optimize.golden(f, brack=(-1, 0.5, 2))
>>> minimum
-1.5717277788484873e-162
"""
options = {'xtol': tol, 'maxiter': maxiter}
res = _minimize_scalar_golden(func, brack, args, **options)
if full_output:
return res['x'], res['fun'], res['nfev']
else:
return res['x']
def _minimize_scalar_golden(func, brack=None, args=(),
xtol=_epsilon, maxiter=5000, **unknown_options):
"""
Options
-------
maxiter : int
Maximum number of iterations to perform.
xtol : float
Relative error in solution `xopt` acceptable for convergence.
"""
_check_unknown_options(unknown_options)
tol = xtol
if brack is None:
xa, xb, xc, fa, fb, fc, funcalls = bracket(func, args=args)
elif len(brack) == 2:
xa, xb, xc, fa, fb, fc, funcalls = bracket(func, xa=brack[0],
xb=brack[1], args=args)
elif len(brack) == 3:
xa, xb, xc = brack
if (xa > xc): # swap so xa < xc can be assumed
xc, xa = xa, xc
if not ((xa < xb) and (xb < xc)):
raise ValueError("Not a bracketing interval.")
fa = func(*((xa,) + args))
fb = func(*((xb,) + args))
fc = func(*((xc,) + args))
if not ((fb < fa) and (fb < fc)):
raise ValueError("Not a bracketing interval.")
funcalls = 3
else:
raise ValueError("Bracketing interval must be length 2 or 3 sequence.")
_gR = 0.61803399 # golden ratio conjugate: 2.0/(1.0+sqrt(5.0))
_gC = 1.0 - _gR
x3 = xc
x0 = xa
if (numpy.abs(xc - xb) > numpy.abs(xb - xa)):
x1 = xb
x2 = xb + _gC * (xc - xb)
else:
x2 = xb
x1 = xb - _gC * (xb - xa)
f1 = func(*((x1,) + args))
f2 = func(*((x2,) + args))
funcalls += 2
nit = 0
for i in xrange(maxiter):
if numpy.abs(x3 - x0) <= tol * (numpy.abs(x1) + numpy.abs(x2)):
break
if (f2 < f1):
x0 = x1
x1 = x2
x2 = _gR * x1 + _gC * x3
f1 = f2
f2 = func(*((x2,) + args))
else:
x3 = x2
x2 = x1
x1 = _gR * x2 + _gC * x0
f2 = f1
f1 = func(*((x1,) + args))
funcalls += 1
nit += 1
if (f1 < f2):
xmin = x1
fval = f1
else:
xmin = x2
fval = f2
return OptimizeResult(fun=fval, nfev=funcalls, x=xmin, nit=nit,
success=nit < maxiter)
def bracket(func, xa=0.0, xb=1.0, args=(), grow_limit=110.0, maxiter=1000):
"""
Bracket the minimum of the function.
Given a function and distinct initial points, search in the
downhill direction (as defined by the initital points) and return
new points xa, xb, xc that bracket the minimum of the function
f(xa) > f(xb) < f(xc). It doesn't always mean that obtained
solution will satisfy xa<=x<=xb
Parameters
----------
func : callable f(x,*args)
Objective function to minimize.
xa, xb : float, optional
Bracketing interval. Defaults `xa` to 0.0, and `xb` to 1.0.
args : tuple, optional
Additional arguments (if present), passed to `func`.
grow_limit : float, optional
Maximum grow limit. Defaults to 110.0
maxiter : int, optional
Maximum number of iterations to perform. Defaults to 1000.
Returns
-------
xa, xb, xc : float
Bracket.
fa, fb, fc : float
Objective function values in bracket.
funcalls : int
Number of function evaluations made.
"""
_gold = 1.618034 # golden ratio: (1.0+sqrt(5.0))/2.0
_verysmall_num = 1e-21
fa = func(*(xa,) + args)
fb = func(*(xb,) + args)
if (fa < fb): # Switch so fa > fb
xa, xb = xb, xa
fa, fb = fb, fa
xc = xb + _gold * (xb - xa)
fc = func(*((xc,) + args))
funcalls = 3
iter = 0
while (fc < fb):
tmp1 = (xb - xa) * (fb - fc)
tmp2 = (xb - xc) * (fb - fa)
val = tmp2 - tmp1
if numpy.abs(val) < _verysmall_num:
denom = 2.0 * _verysmall_num
else:
denom = 2.0 * val
w = xb - ((xb - xc) * tmp2 - (xb - xa) * tmp1) / denom
wlim = xb + grow_limit * (xc - xb)
if iter > maxiter:
raise RuntimeError("Too many iterations.")
iter += 1
if (w - xc) * (xb - w) > 0.0:
fw = func(*((w,) + args))
funcalls += 1
if (fw < fc):
xa = xb
xb = w
fa = fb
fb = fw
return xa, xb, xc, fa, fb, fc, funcalls
elif (fw > fb):
xc = w
fc = fw
return xa, xb, xc, fa, fb, fc, funcalls
w = xc + _gold * (xc - xb)
fw = func(*((w,) + args))
funcalls += 1
elif (w - wlim)*(wlim - xc) >= 0.0:
w = wlim
fw = func(*((w,) + args))
funcalls += 1
elif (w - wlim)*(xc - w) > 0.0:
fw = func(*((w,) + args))
funcalls += 1
if (fw < fc):
xb = xc
xc = w
w = xc + _gold * (xc - xb)
fb = fc
fc = fw
fw = func(*((w,) + args))
funcalls += 1
else:
w = xc + _gold * (xc - xb)
fw = func(*((w,) + args))
funcalls += 1
xa = xb
xb = xc
xc = w
fa = fb
fb = fc
fc = fw
return xa, xb, xc, fa, fb, fc, funcalls
def _linesearch_powell(func, p, xi, tol=1e-3):
"""Line-search algorithm using fminbound.
Find the minimium of the function ``func(x0+ alpha*direc)``.
"""
def myfunc(alpha):
return func(p + alpha*xi)
alpha_min, fret, iter, num = brent(myfunc, full_output=1, tol=tol)
xi = alpha_min*xi
return squeeze(fret), p + xi, xi
def fmin_powell(func, x0, args=(), xtol=1e-4, ftol=1e-4, maxiter=None,
maxfun=None, full_output=0, disp=1, retall=0, callback=None,
direc=None):
"""
Minimize a function using modified Powell's method. This method
only uses function values, not derivatives.
Parameters
----------
func : callable f(x,*args)
Objective function to be minimized.
x0 : ndarray
Initial guess.
args : tuple, optional
Extra arguments passed to func.
callback : callable, optional
An optional user-supplied function, called after each
iteration. Called as ``callback(xk)``, where ``xk`` is the
current parameter vector.
direc : ndarray, optional
Initial direction set.
xtol : float, optional
Line-search error tolerance.
ftol : float, optional
Relative error in ``func(xopt)`` acceptable for convergence.
maxiter : int, optional
Maximum number of iterations to perform.
maxfun : int, optional
Maximum number of function evaluations to make.
full_output : bool, optional
If True, fopt, xi, direc, iter, funcalls, and
warnflag are returned.
disp : bool, optional
If True, print convergence messages.
retall : bool, optional
If True, return a list of the solution at each iteration.
Returns
-------
xopt : ndarray
Parameter which minimizes `func`.
fopt : number
Value of function at minimum: ``fopt = func(xopt)``.
direc : ndarray
Current direction set.
iter : int
Number of iterations.
funcalls : int
Number of function calls made.
warnflag : int
Integer warning flag:
1 : Maximum number of function evaluations.
2 : Maximum number of iterations.
allvecs : list
List of solutions at each iteration.
See also
--------
minimize: Interface to unconstrained minimization algorithms for
multivariate functions. See the 'Powell' `method` in particular.
Notes
-----
Uses a modification of Powell's method to find the minimum of
a function of N variables. Powell's method is a conjugate
direction method.
The algorithm has two loops. The outer loop
merely iterates over the inner loop. The inner loop minimizes
over each current direction in the direction set. At the end
of the inner loop, if certain conditions are met, the direction
that gave the largest decrease is dropped and replaced with
the difference between the current estimated x and the estimated
x from the beginning of the inner-loop.
The technical conditions for replacing the direction of greatest
increase amount to checking that
1. No further gain can be made along the direction of greatest increase
from that iteration.
2. The direction of greatest increase accounted for a large sufficient
fraction of the decrease in the function value from that iteration of
the inner loop.
Examples
--------
>>> def f(x):
... return x**2
>>> from scipy import optimize
>>> minimum = optimize.fmin_powell(f, -1)
Optimization terminated successfully.
Current function value: 0.000000
Iterations: 2
Function evaluations: 18
>>> minimum
array(0.0)
References
----------
Powell M.J.D. (1964) An efficient method for finding the minimum of a
function of several variables without calculating derivatives,
Computer Journal, 7 (2):155-162.
Press W., Teukolsky S.A., Vetterling W.T., and Flannery B.P.:
Numerical Recipes (any edition), Cambridge University Press
"""
opts = {'xtol': xtol,
'ftol': ftol,
'maxiter': maxiter,
'maxfev': maxfun,
'disp': disp,
'direc': direc,
'return_all': retall}
res = _minimize_powell(func, x0, args, callback=callback, **opts)
if full_output:
retlist = (res['x'], res['fun'], res['direc'], res['nit'],
res['nfev'], res['status'])
if retall:
retlist += (res['allvecs'], )
return retlist
else:
if retall:
return res['x'], res['allvecs']
else:
return res['x']
def _minimize_powell(func, x0, args=(), callback=None,
xtol=1e-4, ftol=1e-4, maxiter=None, maxfev=None,
disp=False, direc=None, return_all=False,
**unknown_options):
"""
Minimization of scalar function of one or more variables using the
modified Powell algorithm.
Options
-------
disp : bool
Set to True to print convergence messages.
xtol : float
Relative error in solution `xopt` acceptable for convergence.
ftol : float
Relative error in ``fun(xopt)`` acceptable for convergence.
maxiter, maxfev : int
Maximum allowed number of iterations and function evaluations.
Will default to ``N*1000``, where ``N`` is the number of
variables, if neither `maxiter` or `maxfev` is set. If both
`maxiter` and `maxfev` are set, minimization will stop at the
first reached.
direc : ndarray
Initial set of direction vectors for the Powell method.
"""
_check_unknown_options(unknown_options)
maxfun = maxfev
retall = return_all
# we need to use a mutable object here that we can update in the
# wrapper function
fcalls, func = wrap_function(func, args)
x = asarray(x0).flatten()
if retall:
allvecs = [x]
N = len(x)
# If neither are set, then set both to default
if maxiter is None and maxfun is None:
maxiter = N * 1000
maxfun = N * 1000
elif maxiter is None:
# Convert remaining Nones, to np.inf, unless the other is np.inf, in
# which case use the default to avoid unbounded iteration
if maxfun == np.inf:
maxiter = N * 1000
else:
maxiter = np.inf
elif maxfun is None:
if maxiter == np.inf:
maxfun = N * 1000
else:
maxfun = np.inf
if direc is None:
direc = eye(N, dtype=float)
else:
direc = asarray(direc, dtype=float)
fval = squeeze(func(x))
x1 = x.copy()
iter = 0
ilist = list(range(N))
while True:
fx = fval
bigind = 0
delta = 0.0
for i in ilist:
direc1 = direc[i]
fx2 = fval
fval, x, direc1 = _linesearch_powell(func, x, direc1,
tol=xtol * 100)
if (fx2 - fval) > delta:
delta = fx2 - fval
bigind = i
iter += 1
if callback is not None:
callback(x)
if retall:
allvecs.append(x)
bnd = ftol * (numpy.abs(fx) + numpy.abs(fval)) + 1e-20
if 2.0 * (fx - fval) <= bnd:
break
if fcalls[0] >= maxfun:
break
if iter >= maxiter:
break
# Construct the extrapolated point
direc1 = x - x1
x2 = 2*x - x1
x1 = x.copy()
fx2 = squeeze(func(x2))
if (fx > fx2):
t = 2.0*(fx + fx2 - 2.0*fval)
temp = (fx - fval - delta)
t *= temp*temp
temp = fx - fx2
t -= delta*temp*temp
if t < 0.0:
fval, x, direc1 = _linesearch_powell(func, x, direc1,
tol=xtol*100)
direc[bigind] = direc[-1]
direc[-1] = direc1
warnflag = 0
if fcalls[0] >= maxfun:
warnflag = 1
msg = _status_message['maxfev']
if disp:
print("Warning: " + msg)
elif iter >= maxiter:
warnflag = 2
msg = _status_message['maxiter']
if disp:
print("Warning: " + msg)
else:
msg = _status_message['success']
if disp:
print(msg)
print(" Current function value: %f" % fval)
print(" Iterations: %d" % iter)
print(" Function evaluations: %d" % fcalls[0])
x = squeeze(x)
result = OptimizeResult(fun=fval, direc=direc, nit=iter, nfev=fcalls[0],
status=warnflag, success=(warnflag == 0),
message=msg, x=x)
if retall:
result['allvecs'] = allvecs
return result
def _endprint(x, flag, fval, maxfun, xtol, disp):
if flag == 0:
if disp > 1:
print("\nOptimization terminated successfully;\n"
"The returned value satisfies the termination criteria\n"
"(using xtol = ", xtol, ")")
if flag == 1:
if disp:
print("\nMaximum number of function evaluations exceeded --- "
"increase maxfun argument.\n")
return
def brute(func, ranges, args=(), Ns=20, full_output=0, finish=fmin,
disp=False):
"""Minimize a function over a given range by brute force.
Uses the "brute force" method, i.e. computes the function's value
at each point of a multidimensional grid of points, to find the global
minimum of the function.
The function is evaluated everywhere in the range with the datatype of the
first call to the function, as enforced by the ``vectorize`` NumPy
function. The value and type of the function evaluation returned when
``full_output=True`` are affected in addition by the ``finish`` argument
(see Notes).
The brute force approach is inefficient because the number of grid points
increases exponentially - the number of grid points to evaluate is
``Ns ** len(x)``. Consequently, even with coarse grid spacing, even
moderately sized problems can take a long time to run, and/or run into
memory limitations.
Parameters
----------
func : callable
The objective function to be minimized. Must be in the
form ``f(x, *args)``, where ``x`` is the argument in
the form of a 1-D array and ``args`` is a tuple of any
additional fixed parameters needed to completely specify
the function.
ranges : tuple
Each component of the `ranges` tuple must be either a
"slice object" or a range tuple of the form ``(low, high)``.
The program uses these to create the grid of points on which
the objective function will be computed. See `Note 2` for
more detail.
args : tuple, optional
Any additional fixed parameters needed to completely specify
the function.
Ns : int, optional
Number of grid points along the axes, if not otherwise
specified. See `Note2`.
full_output : bool, optional
If True, return the evaluation grid and the objective function's
values on it.
finish : callable, optional
An optimization function that is called with the result of brute force
minimization as initial guess. `finish` should take `func` and
the initial guess as positional arguments, and take `args` as
keyword arguments. It may additionally take `full_output`
and/or `disp` as keyword arguments. Use None if no "polishing"
function is to be used. See Notes for more details.
disp : bool, optional
Set to True to print convergence messages.
Returns
-------
x0 : ndarray
A 1-D array containing the coordinates of a point at which the
objective function had its minimum value. (See `Note 1` for
which point is returned.)
fval : float
Function value at the point `x0`. (Returned when `full_output` is
True.)
grid : tuple
Representation of the evaluation grid. It has the same
length as `x0`. (Returned when `full_output` is True.)
Jout : ndarray
Function values at each point of the evaluation
grid, `i.e.`, ``Jout = func(*grid)``. (Returned
when `full_output` is True.)
See Also
--------
basinhopping, differential_evolution
Notes
-----
*Note 1*: The program finds the gridpoint at which the lowest value
of the objective function occurs. If `finish` is None, that is the
point returned. When the global minimum occurs within (or not very far
outside) the grid's boundaries, and the grid is fine enough, that
point will be in the neighborhood of the global minimum.
However, users often employ some other optimization program to
"polish" the gridpoint values, `i.e.`, to seek a more precise
(local) minimum near `brute's` best gridpoint.
The `brute` function's `finish` option provides a convenient way to do
that. Any polishing program used must take `brute's` output as its
initial guess as a positional argument, and take `brute's` input values
for `args` as keyword arguments, otherwise an error will be raised.
It may additionally take `full_output` and/or `disp` as keyword arguments.
`brute` assumes that the `finish` function returns either an
`OptimizeResult` object or a tuple in the form:
``(xmin, Jmin, ... , statuscode)``, where ``xmin`` is the minimizing
value of the argument, ``Jmin`` is the minimum value of the objective
function, "..." may be some other returned values (which are not used
by `brute`), and ``statuscode`` is the status code of the `finish` program.
Note that when `finish` is not None, the values returned are those
of the `finish` program, *not* the gridpoint ones. Consequently,
while `brute` confines its search to the input grid points,
the `finish` program's results usually will not coincide with any
gridpoint, and may fall outside the grid's boundary. Thus, if a
minimum only needs to be found over the provided grid points, make
sure to pass in `finish=None`.
*Note 2*: The grid of points is a `numpy.mgrid` object.
For `brute` the `ranges` and `Ns` inputs have the following effect.
Each component of the `ranges` tuple can be either a slice object or a
two-tuple giving a range of values, such as (0, 5). If the component is a
slice object, `brute` uses it directly. If the component is a two-tuple
range, `brute` internally converts it to a slice object that interpolates
`Ns` points from its low-value to its high-value, inclusive.
Examples
--------
We illustrate the use of `brute` to seek the global minimum of a function
of two variables that is given as the sum of a positive-definite
quadratic and two deep "Gaussian-shaped" craters. Specifically, define
the objective function `f` as the sum of three other functions,
``f = f1 + f2 + f3``. We suppose each of these has a signature
``(z, *params)``, where ``z = (x, y)``, and ``params`` and the functions
are as defined below.
>>> params = (2, 3, 7, 8, 9, 10, 44, -1, 2, 26, 1, -2, 0.5)
>>> def f1(z, *params):
... x, y = z
... a, b, c, d, e, f, g, h, i, j, k, l, scale = params
... return (a * x**2 + b * x * y + c * y**2 + d*x + e*y + f)
>>> def f2(z, *params):
... x, y = z
... a, b, c, d, e, f, g, h, i, j, k, l, scale = params
... return (-g*np.exp(-((x-h)**2 + (y-i)**2) / scale))
>>> def f3(z, *params):
... x, y = z
... a, b, c, d, e, f, g, h, i, j, k, l, scale = params
... return (-j*np.exp(-((x-k)**2 + (y-l)**2) / scale))
>>> def f(z, *params):
... return f1(z, *params) + f2(z, *params) + f3(z, *params)
Thus, the objective function may have local minima near the minimum
of each of the three functions of which it is composed. To
use `fmin` to polish its gridpoint result, we may then continue as
follows:
>>> rranges = (slice(-4, 4, 0.25), slice(-4, 4, 0.25))
>>> from scipy import optimize
>>> resbrute = optimize.brute(f, rranges, args=params, full_output=True,
... finish=optimize.fmin)
>>> resbrute[0] # global minimum
array([-1.05665192, 1.80834843])
>>> resbrute[1] # function value at global minimum
-3.4085818767
Note that if `finish` had been set to None, we would have gotten the
gridpoint [-1.0 1.75] where the rounded function value is -2.892.
"""
N = len(ranges)
if N > 40:
raise ValueError("Brute Force not possible with more "
"than 40 variables.")
lrange = list(ranges)
for k in range(N):
if type(lrange[k]) is not type(slice(None)):
if len(lrange[k]) < 3:
lrange[k] = tuple(lrange[k]) + (complex(Ns),)
lrange[k] = slice(*lrange[k])
if (N == 1):
lrange = lrange[0]
def _scalarfunc(*params):
params = asarray(params).flatten()
return func(params, *args)
vecfunc = vectorize(_scalarfunc)
grid = mgrid[lrange]
if (N == 1):
grid = (grid,)
Jout = vecfunc(*grid)
Nshape = shape(Jout)
indx = argmin(Jout.ravel(), axis=-1)
Nindx = zeros(N, int)
xmin = zeros(N, float)
for k in range(N - 1, -1, -1):
thisN = Nshape[k]
Nindx[k] = indx % Nshape[k]
indx = indx // thisN
for k in range(N):
xmin[k] = grid[k][tuple(Nindx)]
Jmin = Jout[tuple(Nindx)]
if (N == 1):
grid = grid[0]
xmin = xmin[0]
if callable(finish):
# set up kwargs for `finish` function
finish_args = _getargspec(finish).args
finish_kwargs = dict()
if 'full_output' in finish_args:
finish_kwargs['full_output'] = 1
if 'disp' in finish_args:
finish_kwargs['disp'] = disp
elif 'options' in finish_args:
# pass 'disp' as `options`
# (e.g. if `finish` is `minimize`)
finish_kwargs['options'] = {'disp': disp}
# run minimizer
res = finish(func, xmin, args=args, **finish_kwargs)
if isinstance(res, OptimizeResult):
xmin = res.x
Jmin = res.fun
success = res.success
else:
xmin = res[0]
Jmin = res[1]
success = res[-1] == 0
if not success:
if disp:
print("Warning: Either final optimization did not succeed "
"or `finish` does not return `statuscode` as its last "
"argument.")
if full_output:
return xmin, Jmin, grid, Jout
else:
return xmin
def show_options(solver=None, method=None, disp=True):
"""
Show documentation for additional options of optimization solvers.
These are method-specific options that can be supplied through the
``options`` dict.
Parameters
----------
solver : str
Type of optimization solver. One of 'minimize', 'minimize_scalar',
'root', or 'linprog'.
method : str, optional
If not given, shows all methods of the specified solver. Otherwise,
show only the options for the specified method. Valid values
corresponds to methods' names of respective solver (e.g. 'BFGS' for
'minimize').
disp : bool, optional
Whether to print the result rather than returning it.
Returns
-------
text
Either None (for disp=False) or the text string (disp=True)
Notes
-----
The solver-specific methods are:
`scipy.optimize.minimize`
- :ref:`Nelder-Mead <optimize.minimize-neldermead>`
- :ref:`Powell <optimize.minimize-powell>`
- :ref:`CG <optimize.minimize-cg>`
- :ref:`BFGS <optimize.minimize-bfgs>`
- :ref:`Newton-CG <optimize.minimize-newtoncg>`
- :ref:`L-BFGS-B <optimize.minimize-lbfgsb>`
- :ref:`TNC <optimize.minimize-tnc>`
- :ref:`COBYLA <optimize.minimize-cobyla>`
- :ref:`SLSQP <optimize.minimize-slsqp>`
- :ref:`dogleg <optimize.minimize-dogleg>`
- :ref:`trust-ncg <optimize.minimize-trustncg>`
`scipy.optimize.root`
- :ref:`hybr <optimize.root-hybr>`
- :ref:`lm <optimize.root-lm>`
- :ref:`broyden1 <optimize.root-broyden1>`
- :ref:`broyden2 <optimize.root-broyden2>`
- :ref:`anderson <optimize.root-anderson>`
- :ref:`linearmixing <optimize.root-linearmixing>`
- :ref:`diagbroyden <optimize.root-diagbroyden>`
- :ref:`excitingmixing <optimize.root-excitingmixing>`
- :ref:`krylov <optimize.root-krylov>`
- :ref:`df-sane <optimize.root-dfsane>`
`scipy.optimize.minimize_scalar`
- :ref:`brent <optimize.minimize_scalar-brent>`
- :ref:`golden <optimize.minimize_scalar-golden>`
- :ref:`bounded <optimize.minimize_scalar-bounded>`
`scipy.optimize.linprog`
- :ref:`simplex <optimize.linprog-simplex>`
- :ref:`interior-point <optimize.linprog-interior-point>`
"""
import textwrap
doc_routines = {
'minimize': (
('bfgs', 'scipy.optimize.optimize._minimize_bfgs'),
('cg', 'scipy.optimize.optimize._minimize_cg'),
('cobyla', 'scipy.optimize.cobyla._minimize_cobyla'),
('dogleg', 'scipy.optimize._trustregion_dogleg._minimize_dogleg'),
('l-bfgs-b', 'scipy.optimize.lbfgsb._minimize_lbfgsb'),
('nelder-mead', 'scipy.optimize.optimize._minimize_neldermead'),
('newton-cg', 'scipy.optimize.optimize._minimize_newtoncg'),
('powell', 'scipy.optimize.optimize._minimize_powell'),
('slsqp', 'scipy.optimize.slsqp._minimize_slsqp'),
('tnc', 'scipy.optimize.tnc._minimize_tnc'),
('trust-ncg', 'scipy.optimize._trustregion_ncg._minimize_trust_ncg'),
),
'root': (
('hybr', 'scipy.optimize.minpack._root_hybr'),
('lm', 'scipy.optimize._root._root_leastsq'),
('broyden1', 'scipy.optimize._root._root_broyden1_doc'),
('broyden2', 'scipy.optimize._root._root_broyden2_doc'),
('anderson', 'scipy.optimize._root._root_anderson_doc'),
('diagbroyden', 'scipy.optimize._root._root_diagbroyden_doc'),
('excitingmixing', 'scipy.optimize._root._root_excitingmixing_doc'),
('linearmixing', 'scipy.optimize._root._root_linearmixing_doc'),
('krylov', 'scipy.optimize._root._root_krylov_doc'),
('df-sane', 'scipy.optimize._spectral._root_df_sane'),
),
'linprog': (
('simplex', 'scipy.optimize._linprog._linprog_simplex'),
('interior-point', 'scipy.optimize._linprog._linprog_ip'),
),
'minimize_scalar': (
('brent', 'scipy.optimize.optimize._minimize_scalar_brent'),
('bounded', 'scipy.optimize.optimize._minimize_scalar_bounded'),
('golden', 'scipy.optimize.optimize._minimize_scalar_golden'),
),
}
if solver is None:
text = ["\n\n\n========\n", "minimize\n", "========\n"]
text.append(show_options('minimize', disp=False))
text.extend(["\n\n===============\n", "minimize_scalar\n",
"===============\n"])
text.append(show_options('minimize_scalar', disp=False))
text.extend(["\n\n\n====\n", "root\n",
"====\n"])
text.append(show_options('root', disp=False))
text.extend(['\n\n\n=======\n', 'linprog\n',
'=======\n'])
text.append(show_options('linprog', disp=False))
text = "".join(text)
else:
solver = solver.lower()
if solver not in doc_routines:
raise ValueError('Unknown solver %r' % (solver,))
if method is None:
text = []
for name, _ in doc_routines[solver]:
text.extend(["\n\n" + name, "\n" + "="*len(name) + "\n\n"])
text.append(show_options(solver, name, disp=False))
text = "".join(text)
else:
method = method.lower()
methods = dict(doc_routines[solver])
if method not in methods:
raise ValueError("Unknown method %r" % (method,))
name = methods[method]
# Import function object
parts = name.split('.')
mod_name = ".".join(parts[:-1])
__import__(mod_name)
obj = getattr(sys.modules[mod_name], parts[-1])
# Get doc
doc = obj.__doc__
if doc is not None:
text = textwrap.dedent(doc).strip()
else:
text = ""
if disp:
print(text)
return
else:
return text
def main():
import time
times = []
algor = []
x0 = [0.8, 1.2, 0.7]
print("Nelder-Mead Simplex")
print("===================")
start = time.time()
x = fmin(rosen, x0)
print(x)
times.append(time.time() - start)
algor.append('Nelder-Mead Simplex\t')
print()
print("Powell Direction Set Method")
print("===========================")
start = time.time()
x = fmin_powell(rosen, x0)
print(x)
times.append(time.time() - start)
algor.append('Powell Direction Set Method.')
print()
print("Nonlinear CG")
print("============")
start = time.time()
x = fmin_cg(rosen, x0, fprime=rosen_der, maxiter=200)
print(x)
times.append(time.time() - start)
algor.append('Nonlinear CG \t')
print()
print("BFGS Quasi-Newton")
print("=================")
start = time.time()
x = fmin_bfgs(rosen, x0, fprime=rosen_der, maxiter=80)
print(x)
times.append(time.time() - start)
algor.append('BFGS Quasi-Newton\t')
print()
print("BFGS approximate gradient")
print("=========================")
start = time.time()
x = fmin_bfgs(rosen, x0, gtol=1e-4, maxiter=100)
print(x)
times.append(time.time() - start)
algor.append('BFGS without gradient\t')
print()
print("Newton-CG with Hessian product")
print("==============================")
start = time.time()
x = fmin_ncg(rosen, x0, rosen_der, fhess_p=rosen_hess_prod, maxiter=80)
print(x)
times.append(time.time() - start)
algor.append('Newton-CG with hessian product')
print()
print("Newton-CG with full Hessian")
print("===========================")
start = time.time()
x = fmin_ncg(rosen, x0, rosen_der, fhess=rosen_hess, maxiter=80)
print(x)
times.append(time.time() - start)
algor.append('Newton-CG with full hessian')
print()
print("\nMinimizing the Rosenbrock function of order 3\n")
print(" Algorithm \t\t\t Seconds")
print("===========\t\t\t =========")
for k in range(len(algor)):
print(algor[k], "\t -- ", times[k])
if __name__ == "__main__":
main()
| 104,490 | 32.501443 | 90 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_trustregion.py
|
"""Trust-region optimization."""
from __future__ import division, print_function, absolute_import
import math
import numpy as np
import scipy.linalg
from .optimize import (_check_unknown_options, wrap_function, _status_message,
OptimizeResult)
__all__ = []
class BaseQuadraticSubproblem(object):
"""
Base/abstract class defining the quadratic model for trust-region
minimization. Child classes must implement the ``solve`` method.
Values of the objective function, jacobian and hessian (if provided) at
the current iterate ``x`` are evaluated on demand and then stored as
attributes ``fun``, ``jac``, ``hess``.
"""
def __init__(self, x, fun, jac, hess=None, hessp=None):
self._x = x
self._f = None
self._g = None
self._h = None
self._g_mag = None
self._cauchy_point = None
self._newton_point = None
self._fun = fun
self._jac = jac
self._hess = hess
self._hessp = hessp
def __call__(self, p):
return self.fun + np.dot(self.jac, p) + 0.5 * np.dot(p, self.hessp(p))
@property
def fun(self):
"""Value of objective function at current iteration."""
if self._f is None:
self._f = self._fun(self._x)
return self._f
@property
def jac(self):
"""Value of jacobian of objective function at current iteration."""
if self._g is None:
self._g = self._jac(self._x)
return self._g
@property
def hess(self):
"""Value of hessian of objective function at current iteration."""
if self._h is None:
self._h = self._hess(self._x)
return self._h
def hessp(self, p):
if self._hessp is not None:
return self._hessp(self._x, p)
else:
return np.dot(self.hess, p)
@property
def jac_mag(self):
"""Magniture of jacobian of objective function at current iteration."""
if self._g_mag is None:
self._g_mag = scipy.linalg.norm(self.jac)
return self._g_mag
def get_boundaries_intersections(self, z, d, trust_radius):
"""
Solve the scalar quadratic equation ||z + t d|| == trust_radius.
This is like a line-sphere intersection.
Return the two values of t, sorted from low to high.
"""
a = np.dot(d, d)
b = 2 * np.dot(z, d)
c = np.dot(z, z) - trust_radius**2
sqrt_discriminant = math.sqrt(b*b - 4*a*c)
# The following calculation is mathematically
# equivalent to:
# ta = (-b - sqrt_discriminant) / (2*a)
# tb = (-b + sqrt_discriminant) / (2*a)
# but produce smaller round off errors.
# Look at Matrix Computation p.97
# for a better justification.
aux = b + math.copysign(sqrt_discriminant, b)
ta = -aux / (2*a)
tb = -2*c / aux
return sorted([ta, tb])
def solve(self, trust_radius):
raise NotImplementedError('The solve method should be implemented by '
'the child class')
def _minimize_trust_region(fun, x0, args=(), jac=None, hess=None, hessp=None,
subproblem=None, initial_trust_radius=1.0,
max_trust_radius=1000.0, eta=0.15, gtol=1e-4,
maxiter=None, disp=False, return_all=False,
callback=None, inexact=True, **unknown_options):
"""
Minimization of scalar function of one or more variables using a
trust-region algorithm.
Options for the trust-region algorithm are:
initial_trust_radius : float
Initial trust radius.
max_trust_radius : float
Never propose steps that are longer than this value.
eta : float
Trust region related acceptance stringency for proposed steps.
gtol : float
Gradient norm must be less than `gtol`
before successful termination.
maxiter : int
Maximum number of iterations to perform.
disp : bool
If True, print convergence message.
inexact : bool
Accuracy to solve subproblems. If True requires less nonlinear
iterations, but more vector products. Only effective for method
trust-krylov.
This function is called by the `minimize` function.
It is not supposed to be called directly.
"""
_check_unknown_options(unknown_options)
if jac is None:
raise ValueError('Jacobian is currently required for trust-region '
'methods')
if hess is None and hessp is None:
raise ValueError('Either the Hessian or the Hessian-vector product '
'is currently required for trust-region methods')
if subproblem is None:
raise ValueError('A subproblem solving strategy is required for '
'trust-region methods')
if not (0 <= eta < 0.25):
raise Exception('invalid acceptance stringency')
if max_trust_radius <= 0:
raise Exception('the max trust radius must be positive')
if initial_trust_radius <= 0:
raise ValueError('the initial trust radius must be positive')
if initial_trust_radius >= max_trust_radius:
raise ValueError('the initial trust radius must be less than the '
'max trust radius')
# force the initial guess into a nice format
x0 = np.asarray(x0).flatten()
# Wrap the functions, for a couple reasons.
# This tracks how many times they have been called
# and it automatically passes the args.
nfun, fun = wrap_function(fun, args)
njac, jac = wrap_function(jac, args)
nhess, hess = wrap_function(hess, args)
nhessp, hessp = wrap_function(hessp, args)
# limit the number of iterations
if maxiter is None:
maxiter = len(x0)*200
# init the search status
warnflag = 0
# initialize the search
trust_radius = initial_trust_radius
x = x0
if return_all:
allvecs = [x]
m = subproblem(x, fun, jac, hess, hessp)
k = 0
# search for the function min
# do not even start if the gradient is small enough
while m.jac_mag >= gtol:
# Solve the sub-problem.
# This gives us the proposed step relative to the current position
# and it tells us whether the proposed step
# has reached the trust region boundary or not.
try:
p, hits_boundary = m.solve(trust_radius)
except np.linalg.linalg.LinAlgError as e:
warnflag = 3
break
# calculate the predicted value at the proposed point
predicted_value = m(p)
# define the local approximation at the proposed point
x_proposed = x + p
m_proposed = subproblem(x_proposed, fun, jac, hess, hessp)
# evaluate the ratio defined in equation (4.4)
actual_reduction = m.fun - m_proposed.fun
predicted_reduction = m.fun - predicted_value
if predicted_reduction <= 0:
warnflag = 2
break
rho = actual_reduction / predicted_reduction
# update the trust radius according to the actual/predicted ratio
if rho < 0.25:
trust_radius *= 0.25
elif rho > 0.75 and hits_boundary:
trust_radius = min(2*trust_radius, max_trust_radius)
# if the ratio is high enough then accept the proposed step
if rho > eta:
x = x_proposed
m = m_proposed
# append the best guess, call back, increment the iteration count
if return_all:
allvecs.append(np.copy(x))
if callback is not None:
callback(np.copy(x))
k += 1
# check if the gradient is small enough to stop
if m.jac_mag < gtol:
warnflag = 0
break
# check if we have looked at enough iterations
if k >= maxiter:
warnflag = 1
break
# print some stuff if requested
status_messages = (
_status_message['success'],
_status_message['maxiter'],
'A bad approximation caused failure to predict improvement.',
'A linalg error occurred, such as a non-psd Hessian.',
)
if disp:
if warnflag == 0:
print(status_messages[warnflag])
else:
print('Warning: ' + status_messages[warnflag])
print(" Current function value: %f" % m.fun)
print(" Iterations: %d" % k)
print(" Function evaluations: %d" % nfun[0])
print(" Gradient evaluations: %d" % njac[0])
print(" Hessian evaluations: %d" % nhess[0])
result = OptimizeResult(x=x, success=(warnflag == 0), status=warnflag,
fun=m.fun, jac=m.jac, nfev=nfun[0], njev=njac[0],
nhev=nhess[0], nit=k,
message=status_messages[warnflag])
if hess is not None:
result['hess'] = m.hess
if return_all:
result['allvecs'] = allvecs
return result
| 9,226 | 33.558052 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_minimize.py
|
"""
Unified interfaces to minimization algorithms.
Functions
---------
- minimize : minimization of a function of several variables.
- minimize_scalar : minimization of a function of one variable.
"""
from __future__ import division, print_function, absolute_import
__all__ = ['minimize', 'minimize_scalar']
from warnings import warn
import numpy as np
from scipy._lib.six import callable
from scipy.sparse.linalg import LinearOperator
# unconstrained minimization
from .optimize import (_minimize_neldermead, _minimize_powell, _minimize_cg,
_minimize_bfgs, _minimize_newtoncg,
_minimize_scalar_brent, _minimize_scalar_bounded,
_minimize_scalar_golden, MemoizeJac)
from ._trustregion_dogleg import _minimize_dogleg
from ._trustregion_ncg import _minimize_trust_ncg
from ._trustregion_krylov import _minimize_trust_krylov
from ._trustregion_exact import _minimize_trustregion_exact
from ._trustregion_constr import _minimize_trustregion_constr
from ._constraints import Bounds, new_bounds_to_old, old_bound_to_new
# constrained minimization
from .lbfgsb import _minimize_lbfgsb
from .tnc import _minimize_tnc
from .cobyla import _minimize_cobyla
from .slsqp import _minimize_slsqp
def minimize(fun, x0, args=(), method=None, jac=None, hess=None,
hessp=None, bounds=None, constraints=(), tol=None,
callback=None, options=None):
"""Minimization of scalar function of one or more variables.
Parameters
----------
fun : callable
The objective function to be minimized.
``fun(x, *args) -> float``
where x is an 1-D array with shape (n,) and `args`
is a tuple of the fixed parameters needed to completely
specify the function.
x0 : ndarray, shape (n,)
Initial guess. Array of real elements of size (n,),
where 'n' is the number of independent variables.
args : tuple, optional
Extra arguments passed to the objective function and its
derivatives (`fun`, `jac` and `hess` functions).
method : str or callable, optional
Type of solver. Should be one of
- 'Nelder-Mead' :ref:`(see here) <optimize.minimize-neldermead>`
- 'Powell' :ref:`(see here) <optimize.minimize-powell>`
- 'CG' :ref:`(see here) <optimize.minimize-cg>`
- 'BFGS' :ref:`(see here) <optimize.minimize-bfgs>`
- 'Newton-CG' :ref:`(see here) <optimize.minimize-newtoncg>`
- 'L-BFGS-B' :ref:`(see here) <optimize.minimize-lbfgsb>`
- 'TNC' :ref:`(see here) <optimize.minimize-tnc>`
- 'COBYLA' :ref:`(see here) <optimize.minimize-cobyla>`
- 'SLSQP' :ref:`(see here) <optimize.minimize-slsqp>`
- 'trust-constr':ref:`(see here) <optimize.minimize-trustconstr>`
- 'dogleg' :ref:`(see here) <optimize.minimize-dogleg>`
- 'trust-ncg' :ref:`(see here) <optimize.minimize-trustncg>`
- 'trust-exact' :ref:`(see here) <optimize.minimize-trustexact>`
- 'trust-krylov' :ref:`(see here) <optimize.minimize-trustkrylov>`
- custom - a callable object (added in version 0.14.0),
see below for description.
If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``,
depending if the problem has constraints or bounds.
jac : {callable, '2-point', '3-point', 'cs', bool}, optional
Method for computing the gradient vector. Only for CG, BFGS,
Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov,
trust-exact and trust-constr. If it is a callable, it should be a
function that returns the gradient vector:
``jac(x, *args) -> array_like, shape (n,)``
where x is an array with shape (n,) and `args` is a tuple with
the fixed parameters. Alternatively, the keywords
{'2-point', '3-point', 'cs'} select a finite
difference scheme for numerical estimation of the gradient. Options
'3-point' and 'cs' are available only to 'trust-constr'.
If `jac` is a Boolean and is True, `fun` is assumed to return the
gradient along with the objective function. If False, the gradient
will be estimated using '2-point' finite difference estimation.
hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy}, optional
Method for computing the Hessian matrix. Only for Newton-CG, dogleg,
trust-ncg, trust-krylov, trust-exact and trust-constr. If it is
callable, it should return the Hessian matrix:
``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)``
where x is a (n,) ndarray and `args` is a tuple with the fixed
parameters. LinearOperator and sparse matrix returns are
allowed only for 'trust-constr' method. Alternatively, the keywords
{'2-point', '3-point', 'cs'} select a finite difference scheme
for numerical estimation. Or, objects implementing
`HessianUpdateStrategy` interface can be used to approximate
the Hessian. Available quasi-Newton methods implementing
this interface are:
- `BFGS`;
- `SR1`.
Whenever the gradient is estimated via finite-differences,
the Hessian cannot be estimated with options
{'2-point', '3-point', 'cs'} and needs to be
estimated using one of the quasi-Newton strategies.
Finite-difference options {'2-point', '3-point', 'cs'} and
`HessianUpdateStrategy` are available only for 'trust-constr' method.
hessp : callable, optional
Hessian of objective function times an arbitrary vector p. Only for
Newton-CG, trust-ncg, trust-krylov, trust-constr.
Only one of `hessp` or `hess` needs to be given. If `hess` is
provided, then `hessp` will be ignored. `hessp` must compute the
Hessian times an arbitrary vector:
``hessp(x, p, *args) -> ndarray shape (n,)``
where x is a (n,) ndarray, p is an arbitrary vector with
dimension (n,) and `args` is a tuple with the fixed
parameters.
bounds : sequence or `Bounds`, optional
Bounds on variables for L-BFGS-B, TNC, SLSQP and
trust-constr methods. There are two ways to specify the bounds:
1. Instance of `Bounds` class.
2. Sequence of ``(min, max)`` pairs for each element in `x`. None
is used to specify no bound.
constraints : {Constraint, dict} or List of {Constraint, dict}, optional
Constraints definition (only for COBYLA, SLSQP and trust-constr).
Constraints for 'trust-constr' are defined as a single object or a
list of objects specifying constraints to the optimization problem.
Available constraints are:
- `LinearConstraint`
- `NonlinearConstraint`
Constraints for COBYLA, SLSQP are defined as a list of dictionaries.
Each dictionary with fields:
type : str
Constraint type: 'eq' for equality, 'ineq' for inequality.
fun : callable
The function defining the constraint.
jac : callable, optional
The Jacobian of `fun` (only for SLSQP).
args : sequence, optional
Extra arguments to be passed to the function and Jacobian.
Equality constraint means that the constraint function result is to
be zero whereas inequality means that it is to be non-negative.
Note that COBYLA only supports inequality constraints.
tol : float, optional
Tolerance for termination. For detailed control, use solver-specific
options.
options : dict, optional
A dictionary of solver options. All methods accept the following
generic options:
maxiter : int
Maximum number of iterations to perform.
disp : bool
Set to True to print convergence messages.
For method-specific options, see :func:`show_options()`.
callback : callable, optional
Called after each iteration. For 'trust-constr' it is a callable with
the signature:
``callback(xk, OptimizeResult state) -> bool``
where ``xk`` is the current parameter vector. and ``state``
is an `OptimizeResult` object, with the same fields
as the ones from the return. If callback returns True
the algorithm execution is terminated.
For all the other methods, the signature is:
``callback(xk)``
where ``xk`` is the current parameter vector.
Returns
-------
res : OptimizeResult
The optimization result represented as a ``OptimizeResult`` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. See
`OptimizeResult` for a description of other attributes.
See also
--------
minimize_scalar : Interface to minimization algorithms for scalar
univariate functions
show_options : Additional options accepted by the solvers
Notes
-----
This section describes the available solvers that can be selected by the
'method' parameter. The default method is *BFGS*.
**Unconstrained minimization**
Method :ref:`Nelder-Mead <optimize.minimize-neldermead>` uses the
Simplex algorithm [1]_, [2]_. This algorithm is robust in many
applications. However, if numerical computation of derivative can be
trusted, other algorithms using the first and/or second derivatives
information might be preferred for their better performance in
general.
Method :ref:`Powell <optimize.minimize-powell>` is a modification
of Powell's method [3]_, [4]_ which is a conjugate direction
method. It performs sequential one-dimensional minimizations along
each vector of the directions set (`direc` field in `options` and
`info`), which is updated at each iteration of the main
minimization loop. The function need not be differentiable, and no
derivatives are taken.
Method :ref:`CG <optimize.minimize-cg>` uses a nonlinear conjugate
gradient algorithm by Polak and Ribiere, a variant of the
Fletcher-Reeves method described in [5]_ pp. 120-122. Only the
first derivatives are used.
Method :ref:`BFGS <optimize.minimize-bfgs>` uses the quasi-Newton
method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) [5]_
pp. 136. It uses the first derivatives only. BFGS has proven good
performance even for non-smooth optimizations. This method also
returns an approximation of the Hessian inverse, stored as
`hess_inv` in the OptimizeResult object.
Method :ref:`Newton-CG <optimize.minimize-newtoncg>` uses a
Newton-CG algorithm [5]_ pp. 168 (also known as the truncated
Newton method). It uses a CG method to the compute the search
direction. See also *TNC* method for a box-constrained
minimization with a similar algorithm. Suitable for large-scale
problems.
Method :ref:`dogleg <optimize.minimize-dogleg>` uses the dog-leg
trust-region algorithm [5]_ for unconstrained minimization. This
algorithm requires the gradient and Hessian; furthermore the
Hessian is required to be positive definite.
Method :ref:`trust-ncg <optimize.minimize-trustncg>` uses the
Newton conjugate gradient trust-region algorithm [5]_ for
unconstrained minimization. This algorithm requires the gradient
and either the Hessian or a function that computes the product of
the Hessian with a given vector. Suitable for large-scale problems.
Method :ref:`trust-krylov <optimize.minimize-trustkrylov>` uses
the Newton GLTR trust-region algorithm [14]_, [15]_ for unconstrained
minimization. This algorithm requires the gradient
and either the Hessian or a function that computes the product of
the Hessian with a given vector. Suitable for large-scale problems.
On indefinite problems it requires usually less iterations than the
`trust-ncg` method and is recommended for medium and large-scale problems.
Method :ref:`trust-exact <optimize.minimize-trustexact>`
is a trust-region method for unconstrained minimization in which
quadratic subproblems are solved almost exactly [13]_. This
algorithm requires the gradient and the Hessian (which is
*not* required to be positive definite). It is, in many
situations, the Newton method to converge in fewer iteraction
and the most recommended for small and medium-size problems.
**Bound-Constrained minimization**
Method :ref:`L-BFGS-B <optimize.minimize-lbfgsb>` uses the L-BFGS-B
algorithm [6]_, [7]_ for bound constrained minimization.
Method :ref:`TNC <optimize.minimize-tnc>` uses a truncated Newton
algorithm [5]_, [8]_ to minimize a function with variables subject
to bounds. This algorithm uses gradient information; it is also
called Newton Conjugate-Gradient. It differs from the *Newton-CG*
method described above as it wraps a C implementation and allows
each variable to be given upper and lower bounds.
**Constrained Minimization**
Method :ref:`COBYLA <optimize.minimize-cobyla>` uses the
Constrained Optimization BY Linear Approximation (COBYLA) method
[9]_, [10]_, [11]_. The algorithm is based on linear
approximations to the objective function and each constraint. The
method wraps a FORTRAN implementation of the algorithm. The
constraints functions 'fun' may return either a single number
or an array or list of numbers.
Method :ref:`SLSQP <optimize.minimize-slsqp>` uses Sequential
Least SQuares Programming to minimize a function of several
variables with any combination of bounds, equality and inequality
constraints. The method wraps the SLSQP Optimization subroutine
originally implemented by Dieter Kraft [12]_. Note that the
wrapper handles infinite values in bounds by converting them into
large floating values.
Method :ref:`trust-constr <optimize.minimize-trustconstr>` is a
trust-region algorithm for constrained optimization. It swiches
between two implementations depending on the problem definition.
It is the most versatile constrained minimization algorithm
implemented in SciPy and the most appropriate for large-scale problems.
For equality constrained problems it is an implementation of Byrd-Omojokun
Trust-Region SQP method described in [17]_ and in [5]_, p. 549. When
inequality constraints are imposed as well, it swiches to the trust-region
interior point method described in [16]_. This interior point algorithm,
in turn, solves inequality constraints by introducing slack variables
and solving a sequence of equality-constrained barrier problems
for progressively smaller values of the barrier parameter.
The previously described equality constrained SQP method is
used to solve the subproblems with increasing levels of accuracy
as the iterate gets closer to a solution.
**Finite-Difference Options**
For Method :ref:`trust-constr <optimize.minimize-trustconstr>`
the gradient and the Hessian may be approximated using
three finite-difference schemes: {'2-point', '3-point', 'cs'}.
The scheme 'cs' is, potentially, the most accurate but it
requires the function to correctly handles complex inputs and to
be differentiable in the complex plane. The scheme '3-point' is more
accurate than '2-point' but requires twice as much operations.
**Custom minimizers**
It may be useful to pass a custom minimization method, for example
when using a frontend to this method such as `scipy.optimize.basinhopping`
or a different library. You can simply pass a callable as the ``method``
parameter.
The callable is called as ``method(fun, x0, args, **kwargs, **options)``
where ``kwargs`` corresponds to any other parameters passed to `minimize`
(such as `callback`, `hess`, etc.), except the `options` dict, which has
its contents also passed as `method` parameters pair by pair. Also, if
`jac` has been passed as a bool type, `jac` and `fun` are mangled so that
`fun` returns just the function values and `jac` is converted to a function
returning the Jacobian. The method shall return an ``OptimizeResult``
object.
The provided `method` callable must be able to accept (and possibly ignore)
arbitrary parameters; the set of parameters accepted by `minimize` may
expand in future versions and then these parameters will be passed to
the method. You can find an example in the scipy.optimize tutorial.
.. versionadded:: 0.11.0
References
----------
.. [1] Nelder, J A, and R Mead. 1965. A Simplex Method for Function
Minimization. The Computer Journal 7: 308-13.
.. [2] Wright M H. 1996. Direct search methods: Once scorned, now
respectable, in Numerical Analysis 1995: Proceedings of the 1995
Dundee Biennial Conference in Numerical Analysis (Eds. D F
Griffiths and G A Watson). Addison Wesley Longman, Harlow, UK.
191-208.
.. [3] Powell, M J D. 1964. An efficient method for finding the minimum of
a function of several variables without calculating derivatives. The
Computer Journal 7: 155-162.
.. [4] Press W, S A Teukolsky, W T Vetterling and B P Flannery.
Numerical Recipes (any edition), Cambridge University Press.
.. [5] Nocedal, J, and S J Wright. 2006. Numerical Optimization.
Springer New York.
.. [6] Byrd, R H and P Lu and J. Nocedal. 1995. A Limited Memory
Algorithm for Bound Constrained Optimization. SIAM Journal on
Scientific and Statistical Computing 16 (5): 1190-1208.
.. [7] Zhu, C and R H Byrd and J Nocedal. 1997. L-BFGS-B: Algorithm
778: L-BFGS-B, FORTRAN routines for large scale bound constrained
optimization. ACM Transactions on Mathematical Software 23 (4):
550-560.
.. [8] Nash, S G. Newton-Type Minimization Via the Lanczos Method.
1984. SIAM Journal of Numerical Analysis 21: 770-778.
.. [9] Powell, M J D. A direct search optimization method that models
the objective and constraint functions by linear interpolation.
1994. Advances in Optimization and Numerical Analysis, eds. S. Gomez
and J-P Hennart, Kluwer Academic (Dordrecht), 51-67.
.. [10] Powell M J D. Direct search algorithms for optimization
calculations. 1998. Acta Numerica 7: 287-336.
.. [11] Powell M J D. A view of algorithms for optimization without
derivatives. 2007.Cambridge University Technical Report DAMTP
2007/NA03
.. [12] Kraft, D. A software package for sequential quadratic
programming. 1988. Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace
Center -- Institute for Flight Mechanics, Koln, Germany.
.. [13] Conn, A. R., Gould, N. I., and Toint, P. L.
Trust region methods. 2000. Siam. pp. 169-200.
.. [14] F. Lenders, C. Kirches, A. Potschka: "trlib: A vector-free
implementation of the GLTR method for iterative solution of
the trust region problem", https://arxiv.org/abs/1611.04718
.. [15] N. Gould, S. Lucidi, M. Roma, P. Toint: "Solving the
Trust-Region Subproblem using the Lanczos Method",
SIAM J. Optim., 9(2), 504--525, (1999).
.. [16] Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal. 1999.
An interior point algorithm for large-scale nonlinear programming.
SIAM Journal on Optimization 9.4: 877-900.
.. [17] Lalee, Marucha, Jorge Nocedal, and Todd Plantega. 1998. On the
implementation of an algorithm for large-scale equality constrained
optimization. SIAM Journal on Optimization 8.3: 682-706.
Examples
--------
Let us consider the problem of minimizing the Rosenbrock function. This
function (and its respective derivatives) is implemented in `rosen`
(resp. `rosen_der`, `rosen_hess`) in the `scipy.optimize`.
>>> from scipy.optimize import minimize, rosen, rosen_der
A simple application of the *Nelder-Mead* method is:
>>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
>>> res = minimize(rosen, x0, method='Nelder-Mead', tol=1e-6)
>>> res.x
array([ 1., 1., 1., 1., 1.])
Now using the *BFGS* algorithm, using the first derivative and a few
options:
>>> res = minimize(rosen, x0, method='BFGS', jac=rosen_der,
... options={'gtol': 1e-6, 'disp': True})
Optimization terminated successfully.
Current function value: 0.000000
Iterations: 26
Function evaluations: 31
Gradient evaluations: 31
>>> res.x
array([ 1., 1., 1., 1., 1.])
>>> print(res.message)
Optimization terminated successfully.
>>> res.hess_inv
array([[ 0.00749589, 0.01255155, 0.02396251, 0.04750988, 0.09495377], # may vary
[ 0.01255155, 0.02510441, 0.04794055, 0.09502834, 0.18996269],
[ 0.02396251, 0.04794055, 0.09631614, 0.19092151, 0.38165151],
[ 0.04750988, 0.09502834, 0.19092151, 0.38341252, 0.7664427 ],
[ 0.09495377, 0.18996269, 0.38165151, 0.7664427, 1.53713523]])
Next, consider a minimization problem with several constraints (namely
Example 16.4 from [5]_). The objective function is:
>>> fun = lambda x: (x[0] - 1)**2 + (x[1] - 2.5)**2
There are three constraints defined as:
>>> cons = ({'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2},
... {'type': 'ineq', 'fun': lambda x: -x[0] - 2 * x[1] + 6},
... {'type': 'ineq', 'fun': lambda x: -x[0] + 2 * x[1] + 2})
And variables must be positive, hence the following bounds:
>>> bnds = ((0, None), (0, None))
The optimization problem is solved using the SLSQP method as:
>>> res = minimize(fun, (2, 0), method='SLSQP', bounds=bnds,
... constraints=cons)
It should converge to the theoretical solution (1.4 ,1.7).
"""
x0 = np.asarray(x0)
if x0.dtype.kind in np.typecodes["AllInteger"]:
x0 = np.asarray(x0, dtype=float)
if not isinstance(args, tuple):
args = (args,)
if method is None:
# Select automatically
if constraints:
method = 'SLSQP'
elif bounds is not None:
method = 'L-BFGS-B'
else:
method = 'BFGS'
if callable(method):
meth = "_custom"
else:
meth = method.lower()
if options is None:
options = {}
# check if optional parameters are supported by the selected method
# - jac
if meth in ('nelder-mead', 'powell', 'cobyla') and bool(jac):
warn('Method %s does not use gradient information (jac).' % method,
RuntimeWarning)
# - hess
if meth not in ('newton-cg', 'dogleg', 'trust-ncg', 'trust-constr',
'trust-krylov', 'trust-exact', '_custom') and hess is not None:
warn('Method %s does not use Hessian information (hess).' % method,
RuntimeWarning)
# - hessp
if meth not in ('newton-cg', 'dogleg', 'trust-ncg', 'trust-constr',
'trust-krylov', '_custom') \
and hessp is not None:
warn('Method %s does not use Hessian-vector product '
'information (hessp).' % method, RuntimeWarning)
# - constraints or bounds
if (meth in ('nelder-mead', 'powell', 'cg', 'bfgs', 'newton-cg', 'dogleg',
'trust-ncg') and (bounds is not None or np.any(constraints))):
warn('Method %s cannot handle constraints nor bounds.' % method,
RuntimeWarning)
if meth in ('l-bfgs-b', 'tnc') and np.any(constraints):
warn('Method %s cannot handle constraints.' % method,
RuntimeWarning)
if meth == 'cobyla' and bounds is not None:
warn('Method %s cannot handle bounds.' % method,
RuntimeWarning)
# - callback
if (meth in ('cobyla',) and callback is not None):
warn('Method %s does not support callback.' % method, RuntimeWarning)
# - return_all
if (meth in ('l-bfgs-b', 'tnc', 'cobyla', 'slsqp') and
options.get('return_all', False)):
warn('Method %s does not support the return_all option.' % method,
RuntimeWarning)
# check gradient vector
if meth == 'trust-constr':
if type(jac) is bool:
if jac:
fun = MemoizeJac(fun)
jac = fun.derivative
else:
jac = '2-point'
elif not callable(jac) and jac not in ('2-point', '3-point', 'cs'):
raise ValueError("Unsupported jac definition.")
else:
if jac in ('2-point', '3-point', 'cs'):
if jac in ('3-point', 'cs'):
warn("Only 'trust-constr' method accept %s "
"options for 'jac'. Using '2-point' instead." % jac)
jac = None
elif not callable(jac):
if bool(jac):
fun = MemoizeJac(fun)
jac = fun.derivative
else:
jac = None
# set default tolerances
if tol is not None:
options = dict(options)
if meth == 'nelder-mead':
options.setdefault('xatol', tol)
options.setdefault('fatol', tol)
if meth in ('newton-cg', 'powell', 'tnc'):
options.setdefault('xtol', tol)
if meth in ('powell', 'l-bfgs-b', 'tnc', 'slsqp'):
options.setdefault('ftol', tol)
if meth in ('bfgs', 'cg', 'l-bfgs-b', 'tnc', 'dogleg',
'trust-ncg', 'trust-exact', 'trust-krylov'):
options.setdefault('gtol', tol)
if meth in ('cobyla', '_custom'):
options.setdefault('tol', tol)
if meth == 'trust-constr':
options.setdefault('xtol', tol)
options.setdefault('gtol', tol)
options.setdefault('barrier_tol', tol)
if bounds is not None:
if meth == 'trust-constr':
if not isinstance(bounds, Bounds):
lb, ub = old_bound_to_new(bounds)
bounds = Bounds(lb, ub)
elif meth in ('l-bfgs-b', 'tnc', 'slsqp'):
if isinstance(bounds, Bounds):
bounds = new_bounds_to_old(bounds.lb, bounds.ub, x0.shape[0])
if meth == '_custom':
return method(fun, x0, args=args, jac=jac, hess=hess, hessp=hessp,
bounds=bounds, constraints=constraints,
callback=callback, **options)
elif meth == 'nelder-mead':
return _minimize_neldermead(fun, x0, args, callback, **options)
elif meth == 'powell':
return _minimize_powell(fun, x0, args, callback, **options)
elif meth == 'cg':
return _minimize_cg(fun, x0, args, jac, callback, **options)
elif meth == 'bfgs':
return _minimize_bfgs(fun, x0, args, jac, callback, **options)
elif meth == 'newton-cg':
return _minimize_newtoncg(fun, x0, args, jac, hess, hessp, callback,
**options)
elif meth == 'l-bfgs-b':
return _minimize_lbfgsb(fun, x0, args, jac, bounds,
callback=callback, **options)
elif meth == 'tnc':
return _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,
**options)
elif meth == 'cobyla':
return _minimize_cobyla(fun, x0, args, constraints, **options)
elif meth == 'slsqp':
return _minimize_slsqp(fun, x0, args, jac, bounds,
constraints, callback=callback, **options)
elif meth == 'trust-constr':
return _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp,
bounds, constraints,
callback=callback, **options)
elif meth == 'dogleg':
return _minimize_dogleg(fun, x0, args, jac, hess,
callback=callback, **options)
elif meth == 'trust-ncg':
return _minimize_trust_ncg(fun, x0, args, jac, hess, hessp,
callback=callback, **options)
elif meth == 'trust-krylov':
return _minimize_trust_krylov(fun, x0, args, jac, hess, hessp,
callback=callback, **options)
elif meth == 'trust-exact':
return _minimize_trustregion_exact(fun, x0, args, jac, hess,
callback=callback, **options)
else:
raise ValueError('Unknown solver %s' % method)
def minimize_scalar(fun, bracket=None, bounds=None, args=(),
method='brent', tol=None, options=None):
"""Minimization of scalar function of one variable.
Parameters
----------
fun : callable
Objective function.
Scalar function, must return a scalar.
bracket : sequence, optional
For methods 'brent' and 'golden', `bracket` defines the bracketing
interval and can either have three items ``(a, b, c)`` so that
``a < b < c`` and ``fun(b) < fun(a), fun(c)`` or two items ``a`` and
``c`` which are assumed to be a starting interval for a downhill
bracket search (see `bracket`); it doesn't always mean that the
obtained solution will satisfy ``a <= x <= c``.
bounds : sequence, optional
For method 'bounded', `bounds` is mandatory and must have two items
corresponding to the optimization bounds.
args : tuple, optional
Extra arguments passed to the objective function.
method : str or callable, optional
Type of solver. Should be one of:
- 'Brent' :ref:`(see here) <optimize.minimize_scalar-brent>`
- 'Bounded' :ref:`(see here) <optimize.minimize_scalar-bounded>`
- 'Golden' :ref:`(see here) <optimize.minimize_scalar-golden>`
- custom - a callable object (added in version 0.14.0), see below
tol : float, optional
Tolerance for termination. For detailed control, use solver-specific
options.
options : dict, optional
A dictionary of solver options.
maxiter : int
Maximum number of iterations to perform.
disp : bool
Set to True to print convergence messages.
See :func:`show_options()` for solver-specific options.
Returns
-------
res : OptimizeResult
The optimization result represented as a ``OptimizeResult`` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. See
`OptimizeResult` for a description of other attributes.
See also
--------
minimize : Interface to minimization algorithms for scalar multivariate
functions
show_options : Additional options accepted by the solvers
Notes
-----
This section describes the available solvers that can be selected by the
'method' parameter. The default method is *Brent*.
Method :ref:`Brent <optimize.minimize_scalar-brent>` uses Brent's
algorithm to find a local minimum. The algorithm uses inverse
parabolic interpolation when possible to speed up convergence of
the golden section method.
Method :ref:`Golden <optimize.minimize_scalar-golden>` uses the
golden section search technique. It uses analog of the bisection
method to decrease the bracketed interval. It is usually
preferable to use the *Brent* method.
Method :ref:`Bounded <optimize.minimize_scalar-bounded>` can
perform bounded minimization. It uses the Brent method to find a
local minimum in the interval x1 < xopt < x2.
**Custom minimizers**
It may be useful to pass a custom minimization method, for example
when using some library frontend to minimize_scalar. You can simply
pass a callable as the ``method`` parameter.
The callable is called as ``method(fun, args, **kwargs, **options)``
where ``kwargs`` corresponds to any other parameters passed to `minimize`
(such as `bracket`, `tol`, etc.), except the `options` dict, which has
its contents also passed as `method` parameters pair by pair. The method
shall return an ``OptimizeResult`` object.
The provided `method` callable must be able to accept (and possibly ignore)
arbitrary parameters; the set of parameters accepted by `minimize` may
expand in future versions and then these parameters will be passed to
the method. You can find an example in the scipy.optimize tutorial.
.. versionadded:: 0.11.0
Examples
--------
Consider the problem of minimizing the following function.
>>> def f(x):
... return (x - 2) * x * (x + 2)**2
Using the *Brent* method, we find the local minimum as:
>>> from scipy.optimize import minimize_scalar
>>> res = minimize_scalar(f)
>>> res.x
1.28077640403
Using the *Bounded* method, we find a local minimum with specified
bounds as:
>>> res = minimize_scalar(f, bounds=(-3, -1), method='bounded')
>>> res.x
-2.0000002026
"""
if not isinstance(args, tuple):
args = (args,)
if callable(method):
meth = "_custom"
else:
meth = method.lower()
if options is None:
options = {}
if tol is not None:
options = dict(options)
if meth == 'bounded' and 'xatol' not in options:
warn("Method 'bounded' does not support relative tolerance in x; "
"defaulting to absolute tolerance.", RuntimeWarning)
options['xatol'] = tol
elif meth == '_custom':
options.setdefault('tol', tol)
else:
options.setdefault('xtol', tol)
if meth == '_custom':
return method(fun, args=args, bracket=bracket, bounds=bounds, **options)
elif meth == 'brent':
return _minimize_scalar_brent(fun, bracket, args, **options)
elif meth == 'bounded':
if bounds is None:
raise ValueError('The `bounds` parameter is mandatory for '
'method `bounded`.')
# replace boolean "disp" option, if specified, by an integer value, as
# expected by _minimize_scalar_bounded()
disp = options.get('disp')
if isinstance(disp, bool):
options['disp'] = 2 * int(disp)
return _minimize_scalar_bounded(fun, bounds, args, **options)
elif meth == 'golden':
return _minimize_scalar_golden(fun, bracket, args, **options)
else:
raise ValueError('Unknown solver %s' % method)
| 35,095 | 43.538071 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_linprog_ip.py
|
"""
An interior-point method for linear programming.
"""
# Author: Matt Haberland
from __future__ import print_function, division, absolute_import
import numpy as np
import scipy as sp
import scipy.sparse as sps
from warnings import warn
from scipy.linalg import LinAlgError
from .optimize import OptimizeResult, OptimizeWarning, _check_unknown_options
from scipy.optimize._remove_redundancy import _remove_redundancy
from scipy.optimize._remove_redundancy import _remove_redundancy_sparse
from scipy.optimize._remove_redundancy import _remove_redundancy_dense
def _clean_inputs(
c,
A_ub=None,
b_ub=None,
A_eq=None,
b_eq=None,
bounds=None):
"""
Given user inputs for a linear programming problem, return the
objective vector, upper bound constraints, equality constraints,
and simple bounds in a preferred format.
Parameters
----------
c : array_like
Coefficients of the linear objective function to be minimized.
A_ub : array_like, optional
2-D array which, when matrix-multiplied by ``x``, gives the values of
the upper-bound inequality constraints at ``x``.
b_ub : array_like, optional
1-D array of values representing the upper-bound of each inequality
constraint (row) in ``A_ub``.
A_eq : array_like, optional
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x``.
b_eq : array_like, optional
1-D array of values representing the RHS of each equality constraint
(row) in ``A_eq``.
bounds : sequence, optional
``(min, max)`` pairs for each element in ``x``, defining
the bounds on that parameter. Use None for one of ``min`` or
``max`` when there is no bound in that direction. By default
bounds are ``(0, None)`` (non-negative)
If a sequence containing a single tuple is provided, then ``min`` and
``max`` will be applied to all variables in the problem.
Returns
-------
c : 1-D array
Coefficients of the linear objective function to be minimized.
A_ub : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the upper-bound inequality constraints at ``x``.
b_ub : 1-D array
1-D array of values representing the upper-bound of each inequality
constraint (row) in ``A_ub``.
A_eq : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x``.
b_eq : 1-D array
1-D array of values representing the RHS of each equality constraint
(row) in ``A_eq``.
bounds : sequence of tuples
``(min, max)`` pairs for each element in ``x``, defining
the bounds on that parameter. Use None for each of ``min`` or
``max`` when there is no bound in that direction. By default
bounds are ``(0, None)`` (non-negative)
"""
try:
if c is None:
raise TypeError
try:
c = np.asarray(c, dtype=float).copy().squeeze()
except BaseException: # typically a ValueError and shouldn't be, IMO
raise TypeError
if c.size == 1:
c = c.reshape((-1))
n_x = len(c)
if n_x == 0 or len(c.shape) != 1:
raise ValueError(
"Invalid input for linprog: c should be a 1D array; it must "
"not have more than one non-singleton dimension")
if not(np.isfinite(c).all()):
raise ValueError(
"Invalid input for linprog: c must not contain values "
"inf, nan, or None")
except TypeError:
raise TypeError(
"Invalid input for linprog: c must be a 1D array of numerical "
"coefficients")
try:
try:
if sps.issparse(A_eq) or sps.issparse(A_ub):
A_ub = sps.coo_matrix(
(0, n_x), dtype=float) if A_ub is None else sps.coo_matrix(
A_ub, dtype=float).copy()
else:
A_ub = np.zeros(
(0, n_x), dtype=float) if A_ub is None else np.asarray(
A_ub, dtype=float).copy()
except BaseException:
raise TypeError
n_ub = A_ub.shape[0]
if len(A_ub.shape) != 2 or A_ub.shape[1] != len(c):
raise ValueError(
"Invalid input for linprog: A_ub must have exactly two "
"dimensions, and the number of columns in A_ub must be "
"equal to the size of c ")
if (sps.issparse(A_ub) and not np.isfinite(A_ub.data).all()
or not sps.issparse(A_ub) and not np.isfinite(A_ub).all()):
raise ValueError(
"Invalid input for linprog: A_ub must not contain values "
"inf, nan, or None")
except TypeError:
raise TypeError(
"Invalid input for linprog: A_ub must be a numerical 2D array "
"with each row representing an upper bound inequality constraint")
try:
try:
b_ub = np.array(
[], dtype=float) if b_ub is None else np.asarray(
b_ub, dtype=float).copy().squeeze()
except BaseException:
raise TypeError
if b_ub.size == 1:
b_ub = b_ub.reshape((-1))
if len(b_ub.shape) != 1:
raise ValueError(
"Invalid input for linprog: b_ub should be a 1D array; it "
"must not have more than one non-singleton dimension")
if len(b_ub) != n_ub:
raise ValueError(
"Invalid input for linprog: The number of rows in A_ub must "
"be equal to the number of values in b_ub")
if not(np.isfinite(b_ub).all()):
raise ValueError(
"Invalid input for linprog: b_ub must not contain values "
"inf, nan, or None")
except TypeError:
raise TypeError(
"Invalid input for linprog: b_ub must be a 1D array of "
"numerical values, each representing the upper bound of an "
"inequality constraint (row) in A_ub")
try:
try:
if sps.issparse(A_eq) or sps.issparse(A_ub):
A_eq = sps.coo_matrix(
(0, n_x), dtype=float) if A_eq is None else sps.coo_matrix(
A_eq, dtype=float).copy()
else:
A_eq = np.zeros(
(0, n_x), dtype=float) if A_eq is None else np.asarray(
A_eq, dtype=float).copy()
except BaseException:
raise TypeError
n_eq = A_eq.shape[0]
if len(A_eq.shape) != 2 or A_eq.shape[1] != len(c):
raise ValueError(
"Invalid input for linprog: A_eq must have exactly two "
"dimensions, and the number of columns in A_eq must be "
"equal to the size of c ")
if (sps.issparse(A_eq) and not np.isfinite(A_eq.data).all()
or not sps.issparse(A_eq) and not np.isfinite(A_eq).all()):
raise ValueError(
"Invalid input for linprog: A_eq must not contain values "
"inf, nan, or None")
except TypeError:
raise TypeError(
"Invalid input for linprog: A_eq must be a 2D array with each "
"row representing an equality constraint")
try:
try:
b_eq = np.array(
[], dtype=float) if b_eq is None else np.asarray(
b_eq, dtype=float).copy().squeeze()
except BaseException:
raise TypeError
if b_eq.size == 1:
b_eq = b_eq.reshape((-1))
if len(b_eq.shape) != 1:
raise ValueError(
"Invalid input for linprog: b_eq should be a 1D array; it "
"must not have more than one non-singleton dimension")
if len(b_eq) != n_eq:
raise ValueError(
"Invalid input for linprog: the number of rows in A_eq "
"must be equal to the number of values in b_eq")
if not(np.isfinite(b_eq).all()):
raise ValueError(
"Invalid input for linprog: b_eq must not contain values "
"inf, nan, or None")
except TypeError:
raise TypeError(
"Invalid input for linprog: b_eq must be a 1D array of "
"numerical values, each representing the right hand side of an "
"equality constraints (row) in A_eq")
# "If a sequence containing a single tuple is provided, then min and max
# will be applied to all variables in the problem."
# linprog doesn't treat this right: it didn't accept a list with one tuple
# in it
try:
if isinstance(bounds, str):
raise TypeError
if bounds is None or len(bounds) == 0:
bounds = [(0, None)] * n_x
elif len(bounds) == 1:
b = bounds[0]
if len(b) != 2:
raise ValueError(
"Invalid input for linprog: exactly one lower bound and "
"one upper bound must be specified for each element of x")
bounds = [b] * n_x
elif len(bounds) == n_x:
try:
len(bounds[0])
except BaseException:
bounds = [(bounds[0], bounds[1])] * n_x
for i, b in enumerate(bounds):
if len(b) != 2:
raise ValueError(
"Invalid input for linprog, bound " +
str(i) +
" " +
str(b) +
": exactly one lower bound and one upper bound must "
"be specified for each element of x")
elif (len(bounds) == 2 and np.isreal(bounds[0])
and np.isreal(bounds[1])):
bounds = [(bounds[0], bounds[1])] * n_x
else:
raise ValueError(
"Invalid input for linprog: exactly one lower bound and one "
"upper bound must be specified for each element of x")
clean_bounds = [] # also creates a copy so user's object isn't changed
for i, b in enumerate(bounds):
if b[0] is not None and b[1] is not None and b[0] > b[1]:
raise ValueError(
"Invalid input for linprog, bound " +
str(i) +
" " +
str(b) +
": a lower bound must be less than or equal to the "
"corresponding upper bound")
if b[0] == np.inf:
raise ValueError(
"Invalid input for linprog, bound " +
str(i) +
" " +
str(b) +
": infinity is not a valid lower bound")
if b[1] == -np.inf:
raise ValueError(
"Invalid input for linprog, bound " +
str(i) +
" " +
str(b) +
": negative infinity is not a valid upper bound")
lb = float(b[0]) if b[0] is not None and b[0] != -np.inf else None
ub = float(b[1]) if b[1] is not None and b[1] != np.inf else None
clean_bounds.append((lb, ub))
bounds = clean_bounds
except ValueError as e:
if "could not convert string to float" in e.args[0]:
raise TypeError
else:
raise e
except TypeError as e:
print(e)
raise TypeError(
"Invalid input for linprog: bounds must be a sequence of "
"(min,max) pairs, each defining bounds on an element of x ")
return c, A_ub, b_ub, A_eq, b_eq, bounds
def _presolve(c, A_ub, b_ub, A_eq, b_eq, bounds, rr):
"""
Given inputs for a linear programming problem in preferred format,
presolve the problem: identify trivial infeasibilities, redundancies,
and unboundedness, tighten bounds where possible, and eliminate fixed
variables.
Parameters
----------
c : 1-D array
Coefficients of the linear objective function to be minimized.
A_ub : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the upper-bound inequality constraints at ``x``.
b_ub : 1-D array
1-D array of values representing the upper-bound of each inequality
constraint (row) in ``A_ub``.
A_eq : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x``.
b_eq : 1-D array
1-D array of values representing the RHS of each equality constraint
(row) in ``A_eq``.
bounds : sequence of tuples
``(min, max)`` pairs for each element in ``x``, defining
the bounds on that parameter. Use None for each of ``min`` or
``max`` when there is no bound in that direction.
Returns
-------
c : 1-D array
Coefficients of the linear objective function to be minimized.
c0 : 1-D array
Constant term in objective function due to fixed (and eliminated)
variables.
A_ub : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the upper-bound inequality constraints at ``x``. Unnecessary
rows/columns have been removed.
b_ub : 1-D array
1-D array of values representing the upper-bound of each inequality
constraint (row) in ``A_ub``. Unnecessary elements have been removed.
A_eq : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x``. Unnecessary rows/columns have been
removed.
b_eq : 1-D array
1-D array of values representing the RHS of each equality constraint
(row) in ``A_eq``. Unnecessary elements have been removed.
bounds : sequence of tuples
``(min, max)`` pairs for each element in ``x``, defining
the bounds on that parameter. Use None for each of ``min`` or
``max`` when there is no bound in that direction. Bounds have been
tightened where possible.
x : 1-D array
Solution vector (when the solution is trivial and can be determined
in presolve)
undo: list of tuples
(index, value) pairs that record the original index and fixed value
for each variable removed from the problem
complete: bool
Whether the solution is complete (solved or determined to be infeasible
or unbounded in presolve)
status : int
An integer representing the exit status of the optimization::
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
message : str
A string descriptor of the exit status of the optimization.
References
----------
.. [2] Andersen, Erling D. "Finding all linearly dependent rows in
large-scale linear programming." Optimization Methods and Software
6.3 (1995): 219-227.
.. [5] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear
programming." Mathematical Programming 71.2 (1995): 221-245.
"""
# ideas from Reference [5] by Andersen and Andersen
# however, unlike the reference, this is performed before converting
# problem to standard form
# There are a few advantages:
# * artificial variables have not been added, so matrices are smaller
# * bounds have not been converted to constraints yet. (It is better to
# do that after presolve because presolve may adjust the simple bounds.)
# There are many improvements that can be made, namely:
# * implement remaining checks from [5]
# * loop presolve until no additional changes are made
# * implement additional efficiency improvements in redundancy removal [2]
tol = 1e-9 # tolerance for equality. should this be exposed to user?
undo = [] # record of variables eliminated from problem
# constant term in cost function may be added if variables are eliminated
c0 = 0
complete = False # complete is True if detected infeasible/unbounded
x = np.zeros(c.shape) # this is solution vector if completed in presolve
status = 0 # all OK unless determined otherwise
message = ""
# Standard form for bounds (from _clean_inputs) is list of tuples
# but numpy array is more convenient here
# In retrospect, numpy array should have been the standard
bounds = np.array(bounds)
lb = bounds[:, 0]
ub = bounds[:, 1]
lb[np.equal(lb, None)] = -np.inf
ub[np.equal(ub, None)] = np.inf
bounds = bounds.astype(float)
lb = lb.astype(float)
ub = ub.astype(float)
m_eq, n = A_eq.shape
m_ub, n = A_ub.shape
if (sps.issparse(A_eq)):
A_eq = A_eq.tolil()
A_ub = A_ub.tolil()
def where(A):
return A.nonzero()
vstack = sps.vstack
else:
where = np.where
vstack = np.vstack
# zero row in equality constraints
zero_row = np.array(np.sum(A_eq != 0, axis=1) == 0).flatten()
if np.any(zero_row):
if np.any(
np.logical_and(
zero_row,
np.abs(b_eq) > tol)): # test_zero_row_1
# infeasible if RHS is not zero
status = 2
message = ("The problem is (trivially) infeasible due to a row "
"of zeros in the equality constraint matrix with a "
"nonzero corresponding constraint value.")
complete = True
return (c, c0, A_ub, b_ub, A_eq, b_eq, bounds,
x, undo, complete, status, message)
else: # test_zero_row_2
# if RHS is zero, we can eliminate this equation entirely
A_eq = A_eq[np.logical_not(zero_row), :]
b_eq = b_eq[np.logical_not(zero_row)]
# zero row in inequality constraints
zero_row = np.array(np.sum(A_ub != 0, axis=1) == 0).flatten()
if np.any(zero_row):
if np.any(np.logical_and(zero_row, b_ub < -tol)): # test_zero_row_1
# infeasible if RHS is less than zero (because LHS is zero)
status = 2
message = ("The problem is (trivially) infeasible due to a row "
"of zeros in the equality constraint matrix with a "
"nonzero corresponding constraint value.")
complete = True
return (c, c0, A_ub, b_ub, A_eq, b_eq, bounds,
x, undo, complete, status, message)
else: # test_zero_row_2
# if LHS is >= 0, we can eliminate this constraint entirely
A_ub = A_ub[np.logical_not(zero_row), :]
b_ub = b_ub[np.logical_not(zero_row)]
# zero column in (both) constraints
# this indicates that a variable isn't constrained and can be removed
A = vstack((A_eq, A_ub))
if A.shape[0] > 0:
zero_col = np.array(np.sum(A != 0, axis=0) == 0).flatten()
# variable will be at upper or lower bound, depending on objective
x[np.logical_and(zero_col, c < 0)] = ub[
np.logical_and(zero_col, c < 0)]
x[np.logical_and(zero_col, c > 0)] = lb[
np.logical_and(zero_col, c > 0)]
if np.any(np.isinf(x)): # if an unconstrained variable has no bound
status = 3
message = ("If feasible, the problem is (trivially) unbounded "
"due to a zero column in the constraint matrices. If "
"you wish to check whether the problem is infeasible, "
"turn presolve off.")
complete = True
return (c, c0, A_ub, b_ub, A_eq, b_eq, bounds,
x, undo, complete, status, message)
# variables will equal upper/lower bounds will be removed later
lb[np.logical_and(zero_col, c < 0)] = ub[
np.logical_and(zero_col, c < 0)]
ub[np.logical_and(zero_col, c > 0)] = lb[
np.logical_and(zero_col, c > 0)]
# row singleton in equality constraints
# this fixes a variable and removes the constraint
singleton_row = np.array(np.sum(A_eq != 0, axis=1) == 1).flatten()
rows = where(singleton_row)[0]
cols = where(A_eq[rows, :])[1]
if len(rows) > 0:
for row, col in zip(rows, cols):
val = b_eq[row] / A_eq[row, col]
if not lb[col] - tol <= val <= ub[col] + tol:
# infeasible if fixed value is not within bounds
status = 2
message = ("The problem is (trivially) infeasible because a "
"singleton row in the equality constraints is "
"inconsistent with the bounds.")
complete = True
return (c, c0, A_ub, b_ub, A_eq, b_eq, bounds,
x, undo, complete, status, message)
else:
# sets upper and lower bounds at that fixed value - variable
# will be removed later
lb[col] = val
ub[col] = val
A_eq = A_eq[np.logical_not(singleton_row), :]
b_eq = b_eq[np.logical_not(singleton_row)]
# row singleton in inequality constraints
# this indicates a simple bound and the constraint can be removed
# simple bounds may be adjusted here
# After all of the simple bound information is combined here, get_Abc will
# turn the simple bounds into constraints
singleton_row = np.array(np.sum(A_ub != 0, axis=1) == 1).flatten()
cols = where(A_ub[singleton_row, :])[1]
rows = where(singleton_row)[0]
if len(rows) > 0:
for row, col in zip(rows, cols):
val = b_ub[row] / A_ub[row, col]
if A_ub[row, col] > 0: # upper bound
if val < lb[col] - tol: # infeasible
complete = True
elif val < ub[col]: # new upper bound
ub[col] = val
else: # lower bound
if val > ub[col] + tol: # infeasible
complete = True
elif val > lb[col]: # new lower bound
lb[col] = val
if complete:
status = 2
message = ("The problem is (trivially) infeasible because a "
"singleton row in the upper bound constraints is "
"inconsistent with the bounds.")
return (c, c0, A_ub, b_ub, A_eq, b_eq, bounds,
x, undo, complete, status, message)
A_ub = A_ub[np.logical_not(singleton_row), :]
b_ub = b_ub[np.logical_not(singleton_row)]
# identical bounds indicate that variable can be removed
i_f = np.abs(lb - ub) < tol # indices of "fixed" variables
i_nf = np.logical_not(i_f) # indices of "not fixed" variables
# test_bounds_equal_but_infeasible
if np.all(i_f): # if bounds define solution, check for consistency
residual = b_eq - A_eq.dot(lb)
slack = b_ub - A_ub.dot(lb)
if ((A_ub.size > 0 and np.any(slack < 0)) or
(A_eq.size > 0 and not np.allclose(residual, 0))):
status = 2
message = ("The problem is (trivially) infeasible because the "
"bounds fix all variables to values inconsistent with "
"the constraints")
complete = True
return (c, c0, A_ub, b_ub, A_eq, b_eq, bounds,
x, undo, complete, status, message)
ub_mod = ub
lb_mod = lb
if np.any(i_f):
c0 += c[i_f].dot(lb[i_f])
b_eq = b_eq - A_eq[:, i_f].dot(lb[i_f])
b_ub = b_ub - A_ub[:, i_f].dot(lb[i_f])
c = c[i_nf]
x = x[i_nf]
A_eq = A_eq[:, i_nf]
A_ub = A_ub[:, i_nf]
# record of variables to be added back in
undo = [np.where(i_f)[0], lb[i_f]]
# don't remove these entries from bounds; they'll be used later.
# but we _also_ need a version of the bounds with these removed
lb_mod = lb[i_nf]
ub_mod = ub[i_nf]
# no constraints indicates that problem is trivial
if A_eq.size == 0 and A_ub.size == 0:
b_eq = np.array([])
b_ub = np.array([])
# test_empty_constraint_1
if c.size == 0:
status = 0
message = ("The solution was determined in presolve as there are "
"no non-trivial constraints.")
elif (np.any(np.logical_and(c < 0, ub == np.inf)) or
np.any(np.logical_and(c > 0, lb == -np.inf))):
# test_no_constraints()
status = 3
message = ("If feasible, the problem is (trivially) unbounded "
"because there are no constraints and at least one "
"element of c is negative. If you wish to check "
"whether the problem is infeasible, turn presolve "
"off.")
else: # test_empty_constraint_2
status = 0
message = ("The solution was determined in presolve as there are "
"no non-trivial constraints.")
complete = True
x[c < 0] = ub_mod[c < 0]
x[c > 0] = lb_mod[c > 0]
# if this is not the last step of presolve, should convert bounds back
# to array and return here
# *sigh* - convert bounds back to their standard form (list of tuples)
# again, in retrospect, numpy array would be standard form
lb[np.equal(lb, -np.inf)] = None
ub[np.equal(ub, np.inf)] = None
bounds = np.hstack((lb[:, np.newaxis], ub[:, np.newaxis]))
bounds = bounds.tolist()
for i, row in enumerate(bounds):
for j, col in enumerate(row):
if str(
col) == "nan": # comparing col to float("nan") and
# np.nan doesn't work. should use np.isnan
bounds[i][j] = None
# remove redundant (linearly dependent) rows from equality constraints
n_rows_A = A_eq.shape[0]
redundancy_warning = ("A_eq does not appear to be of full row rank. To "
"improve performance, check the problem formulation "
"for redundant equality constraints.")
if (sps.issparse(A_eq)):
if rr and A_eq.size > 0: # TODO: Fast sparse rank check?
A_eq, b_eq, status, message = _remove_redundancy_sparse(A_eq, b_eq)
if A_eq.shape[0] < n_rows_A:
warn(redundancy_warning, OptimizeWarning)
if status != 0:
complete = True
return (c, c0, A_ub, b_ub, A_eq, b_eq, bounds,
x, undo, complete, status, message)
# This is a wild guess for which redundancy removal algorithm will be
# faster. More testing would be good.
small_nullspace = 5
if rr and A_eq.size > 0:
try: # TODO: instead use results of first SVD in _remove_redundancy
rank = np.linalg.matrix_rank(A_eq)
except: # oh well, we'll have to go with _remove_redundancy_dense
rank = 0
if rr and A_eq.size > 0 and rank < A_eq.shape[0]:
warn(redundancy_warning, OptimizeWarning)
dim_row_nullspace = A_eq.shape[0]-rank
if dim_row_nullspace <= small_nullspace:
A_eq, b_eq, status, message = _remove_redundancy(A_eq, b_eq)
if dim_row_nullspace > small_nullspace or status == 4:
A_eq, b_eq, status, message = _remove_redundancy_dense(A_eq, b_eq)
if A_eq.shape[0] < rank:
message = ("Due to numerical issues, redundant equality "
"constraints could not be removed automatically. "
"Try providing your constraint matrices as sparse "
"matrices to activate sparse presolve, try turning "
"off redundancy removal, or try turning off presolve "
"altogether.")
status = 4
if status != 0:
complete = True
return (c, c0, A_ub, b_ub, A_eq, b_eq, bounds,
x, undo, complete, status, message)
def _get_Abc(
c,
c0=0,
A_ub=None,
b_ub=None,
A_eq=None,
b_eq=None,
bounds=None,
undo=[]):
"""
Given a linear programming problem of the form:
minimize: c^T * x
subject to: A_ub * x <= b_ub
A_eq * x == b_eq
bounds[i][0] < x_i < bounds[i][1]
return the problem in standard form:
minimize: c'^T * x'
subject to: A * x' == b
0 < x' < oo
by adding slack variables and making variable substitutions as necessary.
Parameters
----------
c : 1-D array
Coefficients of the linear objective function to be minimized.
Components corresponding with fixed variables have been eliminated.
c0 : float
Constant term in objective function due to fixed (and eliminated)
variables.
A_ub : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the upper-bound inequality constraints at ``x``. Unnecessary
rows/columns have been removed.
b_ub : 1-D array
1-D array of values representing the upper-bound of each inequality
constraint (row) in ``A_ub``. Unnecessary elements have been removed.
A_eq : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x``. Unnecessary rows/columns have been
removed.
b_eq : 1-D array
1-D array of values representing the RHS of each equality constraint
(row) in ``A_eq``. Unnecessary elements have been removed.
bounds : sequence of tuples
``(min, max)`` pairs for each element in ``x``, defining
the bounds on that parameter. Use None for each of ``min`` or
``max`` when there is no bound in that direction. Bounds have been
tightened where possible.
undo: list of tuples
(`index`, `value`) pairs that record the original index and fixed value
for each variable removed from the problem
Returns
-------
A : 2-D array
2-D array which, when matrix-multiplied by x, gives the values of the
equality constraints at x (for standard form problem).
b : 1-D array
1-D array of values representing the RHS of each equality constraint
(row) in A (for standard form problem).
c : 1-D array
Coefficients of the linear objective function to be minimized (for
standard form problem).
c0 : float
Constant term in objective function due to fixed (and eliminated)
variables.
References
----------
.. [6] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear
programming." Athena Scientific 1 (1997): 997.
"""
if sps.issparse(A_eq):
sparse = True
A_eq = sps.lil_matrix(A_eq)
A_ub = sps.lil_matrix(A_ub)
def hstack(blocks):
return sps.hstack(blocks, format="lil")
def vstack(blocks):
return sps.vstack(blocks, format="lil")
zeros = sps.lil_matrix
eye = sps.eye
else:
sparse = False
hstack = np.hstack
vstack = np.vstack
zeros = np.zeros
eye = np.eye
fixed_x = set()
if len(undo) > 0:
# these are indices of variables removed from the problem
# however, their bounds are still part of the bounds list
fixed_x = set(undo[0])
# they are needed elsewhere, but not here
bounds = [bounds[i] for i in range(len(bounds)) if i not in fixed_x]
# in retrospect, the standard form of bounds should have been an n x 2
# array. maybe change it someday.
# modify problem such that all variables have only non-negativity bounds
bounds = np.array(bounds)
lbs = bounds[:, 0]
ubs = bounds[:, 1]
m_ub, n_ub = A_ub.shape
lb_none = np.equal(lbs, None)
ub_none = np.equal(ubs, None)
lb_some = np.logical_not(lb_none)
ub_some = np.logical_not(ub_none)
# if preprocessing is on, lb == ub can't happen
# if preprocessing is off, then it would be best to convert that
# to an equality constraint, but it's tricky to make the other
# required modifications from inside here.
# unbounded below: substitute xi = -xi' (unbounded above)
l_nolb_someub = np.logical_and(lb_none, ub_some)
i_nolb = np.where(l_nolb_someub)[0]
lbs[l_nolb_someub], ubs[l_nolb_someub] = (
-ubs[l_nolb_someub], lbs[l_nolb_someub])
lb_none = np.equal(lbs, None)
ub_none = np.equal(ubs, None)
lb_some = np.logical_not(lb_none)
ub_some = np.logical_not(ub_none)
c[i_nolb] *= -1
if len(i_nolb) > 0:
if A_ub.shape[0] > 0: # sometimes needed for sparse arrays... weird
A_ub[:, i_nolb] *= -1
if A_eq.shape[0] > 0:
A_eq[:, i_nolb] *= -1
# upper bound: add inequality constraint
i_newub = np.where(ub_some)[0]
ub_newub = ubs[ub_some]
n_bounds = np.count_nonzero(ub_some)
A_ub = vstack((A_ub, zeros((n_bounds, A_ub.shape[1]))))
b_ub = np.concatenate((b_ub, np.zeros(n_bounds)))
A_ub[range(m_ub, A_ub.shape[0]), i_newub] = 1
b_ub[m_ub:] = ub_newub
A1 = vstack((A_ub, A_eq))
b = np.concatenate((b_ub, b_eq))
c = np.concatenate((c, np.zeros((A_ub.shape[0],))))
# unbounded: substitute xi = xi+ + xi-
l_free = np.logical_and(lb_none, ub_none)
i_free = np.where(l_free)[0]
n_free = len(i_free)
A1 = hstack((A1, zeros((A1.shape[0], n_free))))
c = np.concatenate((c, np.zeros(n_free)))
A1[:, range(n_ub, A1.shape[1])] = -A1[:, i_free]
c[np.arange(n_ub, A1.shape[1])] = -c[i_free]
# add slack variables
A2 = vstack([eye(A_ub.shape[0]), zeros((A_eq.shape[0], A_ub.shape[0]))])
A = hstack([A1, A2])
# lower bound: substitute xi = xi' + lb
# now there is a constant term in objective
i_shift = np.where(lb_some)[0]
lb_shift = lbs[lb_some].astype(float)
c0 += np.sum(lb_shift * c[i_shift])
if sparse:
b = b.reshape(-1, 1)
A = A.tocsc()
b -= (A[:, i_shift] * sps.diags(lb_shift)).sum(axis=1)
b = b.ravel()
else:
b -= (A[:, i_shift] * lb_shift).sum(axis=1)
return A, b, c, c0
def _postprocess(
x,
c,
A_ub=None,
b_ub=None,
A_eq=None,
b_eq=None,
bounds=None,
complete=False,
undo=[],
status=0,
message="",
tol=1e-8):
"""
Given solution x to presolved, standard form linear program x, add
fixed variables back into the problem and undo the variable substitutions
to get solution to original linear program. Also, calculate the objective
function value, slack in original upper bound constraints, and residuals
in original equality constraints.
Parameters
----------
x : 1-D array
Solution vector to the standard-form problem.
c : 1-D array
Original coefficients of the linear objective function to be minimized.
A_ub : 2-D array
Original upper bound constraint matrix.
b_ub : 1-D array
Original upper bound constraint vector.
A_eq : 2-D array
Original equality constraint matrix.
b_eq : 1-D array
Original equality constraint vector.
bounds : sequence of tuples
Bounds, as modified in presolve
complete : bool
Whether the solution is was determined in presolve (``True`` if so)
undo: list of tuples
(`index`, `value`) pairs that record the original index and fixed value
for each variable removed from the problem
status : int
An integer representing the exit status of the optimization::
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
4 : Serious numerical difficulties encountered
message : str
A string descriptor of the exit status of the optimization.
tol : float
Termination tolerance; see [1]_ Section 4.5.
Returns
-------
x : 1-D array
Solution vector to original linear programming problem
fun: float
optimal objective value for original problem
slack: 1-D array
The (non-negative) slack in the upper bound constraints, that is,
``b_ub - A_ub * x``
con : 1-D array
The (nominally zero) residuals of the equality constraints, that is,
``b - A_eq * x``
status : int
An integer representing the exit status of the optimization::
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
4 : Serious numerical difficulties encountered
message : str
A string descriptor of the exit status of the optimization.
"""
# note that all the inputs are the ORIGINAL, unmodified versions
# no rows, columns have been removed
# the only exception is bounds; it has been modified
# we need these modified values to undo the variable substitutions
# in retrospect, perhaps this could have been simplified if the "undo"
# variable also contained information for undoing variable substitutions
n_x = len(c)
# we don't have to undo variable substitutions for fixed variables that
# were removed from the problem
no_adjust = set()
# if there were variables removed from the problem, add them back into the
# solution vector
if len(undo) > 0:
no_adjust = set(undo[0])
x = x.tolist()
for i, val in zip(undo[0], undo[1]):
x.insert(i, val)
x = np.array(x)
# now undo variable substitutions
# if "complete", problem was solved in presolve; don't do anything here
if not complete and bounds is not None: # bounds are never none, probably
n_unbounded = 0
for i, b in enumerate(bounds):
if i in no_adjust:
continue
lb, ub = b
if lb is None and ub is None:
n_unbounded += 1
x[i] = x[i] - x[n_x + n_unbounded - 1]
else:
if lb is None:
x[i] = ub - x[i]
else:
x[i] += lb
n_x = len(c)
x = x[:n_x] # all the rest of the variables were artificial
fun = x.dot(c)
slack = b_ub - A_ub.dot(x) # report slack for ORIGINAL UB constraints
# report residuals of ORIGINAL EQ constraints
con = b_eq - A_eq.dot(x)
# Patch for bug #8664. Detecting this sort of issue earlier
# (via abnormalities in the indicators) would be better.
bounds = np.array(bounds) # again, this should have been the standard form
lb = bounds[:, 0]
ub = bounds[:, 1]
lb[np.equal(lb, None)] = -np.inf
ub[np.equal(ub, None)] = np.inf
tol = np.sqrt(tol) # Somewhat arbitrary, but status 5 is very unusual
if status == 0 and ((slack < -tol).any() or (np.abs(con) > tol).any() or
(x < lb - tol).any() or (x > ub + tol).any()):
status = 4
message = ("The solution does not satisfy the constraints, yet "
"no errors were raised and there is no certificate of "
"infeasibility or unboundedness. This is known to occur "
"if the `presolve` option is False and the problem is "
"infeasible. If you uncounter this under different "
"circumstances, please submit a bug report. Otherwise, "
"please enable presolve.")
elif status == 0 and (np.isnan(x).any() or np.isnan(fun) or
np.isnan(slack).any() or np.isnan(con).any()):
status = 4
message = ("Numerical difficulties were encountered but no errors "
"were raised. This is known to occur if the 'presolve' "
"option is False, 'sparse' is True, and A_eq includes "
"redundant rows. If you encounter this under different "
"circumstances, please submit a bug report. Otherwise, "
"remove linearly dependent equations from your equality "
"constraints or enable presolve.")
return x, fun, slack, con, status, message
def _get_solver(sparse=False, lstsq=False, sym_pos=True, cholesky=True):
"""
Given solver options, return a handle to the appropriate linear system
solver.
Parameters
----------
sparse : bool
True if the system to be solved is sparse. This is typically set
True when the original ``A_ub`` and ``A_eq`` arrays are sparse.
lstsq : bool
True if the system is ill-conditioned and/or (nearly) singular and
thus a more robust least-squares solver is desired. This is sometimes
needed as the solution is approached.
sym_pos : bool
True if the system matrix is symmetric positive definite
Sometimes this needs to be set false as the solution is approached,
even when the system should be symmetric positive definite, due to
numerical difficulties.
cholesky : bool
True if the system is to be solved by Cholesky, rather than LU,
decomposition. This is typically faster unless the problem is very
small or prone to numerical difficulties.
Returns
-------
solve : function
Handle to the appropriate solver function
"""
if sparse:
if lstsq or not(sym_pos):
def solve(M, r, sym_pos=False):
return sps.linalg.lsqr(M, r)[0]
else:
# this is not currently used; it is replaced by splu solve
# TODO: expose use of this as an option
def solve(M, r):
return sps.linalg.spsolve(M, r, permc_spec="MMD_AT_PLUS_A")
else:
if lstsq: # sometimes necessary as solution is approached
def solve(M, r):
return sp.linalg.lstsq(M, r)[0]
elif cholesky:
solve = sp.linalg.cho_solve
else:
# this seems to cache the matrix factorization, so solving
# with multiple right hand sides is much faster
def solve(M, r, sym_pos=sym_pos):
return sp.linalg.solve(M, r, sym_pos=sym_pos)
return solve
def _get_delta(
A,
b,
c,
x,
y,
z,
tau,
kappa,
gamma,
eta,
sparse=False,
lstsq=False,
sym_pos=True,
cholesky=True,
pc=True,
ip=False,
permc_spec='MMD_AT_PLUS_A'):
"""
Given standard form problem defined by ``A``, ``b``, and ``c``;
current variable estimates ``x``, ``y``, ``z``, ``tau``, and ``kappa``;
algorithmic parameters ``gamma and ``eta;
and options ``sparse``, ``lstsq``, ``sym_pos``, ``cholesky``, ``pc``
(predictor-corrector), and ``ip`` (initial point improvement),
get the search direction for increments to the variable estimates.
Parameters
----------
As defined in [1], except:
sparse : bool
True if the system to be solved is sparse. This is typically set
True when the original ``A_ub`` and ``A_eq`` arrays are sparse.
lstsq : bool
True if the system is ill-conditioned and/or (nearly) singular and
thus a more robust least-squares solver is desired. This is sometimes
needed as the solution is approached.
sym_pos : bool
True if the system matrix is symmetric positive definite
Sometimes this needs to be set false as the solution is approached,
even when the system should be symmetric positive definite, due to
numerical difficulties.
cholesky : bool
True if the system is to be solved by Cholesky, rather than LU,
decomposition. This is typically faster unless the problem is very
small or prone to numerical difficulties.
pc : bool
True if the predictor-corrector method of Mehrota is to be used. This
is almost always (if not always) beneficial. Even though it requires
the solution of an additional linear system, the factorization
is typically (implicitly) reused so solution is efficient, and the
number of algorithm iterations is typically reduced.
ip : bool
True if the improved initial point suggestion due to [1] section 4.3
is desired. It's unclear whether this is beneficial.
permc_spec : str (default = 'MMD_AT_PLUS_A')
(Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos =
True``.) A matrix is factorized in each iteration of the algorithm.
This option specifies how to permute the columns of the matrix for
sparsity preservation. Acceptable values are:
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering.
This option can impact the convergence of the
interior point algorithm; test different values to determine which
performs best for your problem. For more information, refer to
``scipy.sparse.linalg.splu``.
Returns
-------
Search directions as defined in [1]
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
"""
if A.shape[0] == 0:
# If there are no constraints, some solvers fail (understandably)
# rather than returning empty solution. This gets the job done.
sparse, lstsq, sym_pos, cholesky = False, False, True, False
solve = _get_solver(sparse, lstsq, sym_pos, cholesky)
n_x = len(x)
# [1] Equation 8.8
r_P = b * tau - A.dot(x)
r_D = c * tau - A.T.dot(y) - z
r_G = c.dot(x) - b.transpose().dot(y) + kappa
mu = (x.dot(z) + tau * kappa) / (n_x + 1)
# Assemble M from [1] Equation 8.31
Dinv = x / z
splu = False
if sparse and not lstsq:
# sparse requires Dinv to be diag matrix
M = A.dot(sps.diags(Dinv, 0, format="csc").dot(A.T))
try:
# TODO: should use linalg.factorized instead, but I don't have
# umfpack and therefore cannot test its performance
solve = sps.linalg.splu(M, permc_spec=permc_spec).solve
splu = True
except:
lstsq = True
solve = _get_solver(sparse, lstsq, sym_pos, cholesky)
else:
# dense does not; use broadcasting
M = A.dot(Dinv.reshape(-1, 1) * A.T)
# For some small problems, calling sp.linalg.solve w/ sym_pos = True
# may be faster. I am pretty certain it caches the factorization for
# multiple uses and checks the incoming matrix to see if it's the same as
# the one it already factorized. (I can't explain the speed otherwise.)
if cholesky:
try:
L = sp.linalg.cho_factor(M)
except:
cholesky = False
solve = _get_solver(sparse, lstsq, sym_pos, cholesky)
# pc: "predictor-corrector" [1] Section 4.1
# In development this option could be turned off
# but it always seems to improve performance substantially
n_corrections = 1 if pc else 0
i = 0
alpha, d_x, d_z, d_tau, d_kappa = 0, 0, 0, 0, 0
while i <= n_corrections:
# Reference [1] Eq. 8.6
rhatp = eta(gamma) * r_P
rhatd = eta(gamma) * r_D
rhatg = np.array(eta(gamma) * r_G).reshape((1,))
# Reference [1] Eq. 8.7
rhatxs = gamma * mu - x * z
rhattk = np.array(gamma * mu - tau * kappa).reshape((1,))
if i == 1:
if ip: # if the correction is to get "initial point"
# Reference [1] Eq. 8.23
rhatxs = ((1 - alpha) * gamma * mu -
x * z - alpha**2 * d_x * d_z)
rhattk = np.array(
(1 -
alpha) *
gamma *
mu -
tau *
kappa -
alpha**2 *
d_tau *
d_kappa).reshape(
(1,
))
else: # if the correction is for "predictor-corrector"
# Reference [1] Eq. 8.13
rhatxs -= d_x * d_z
rhattk -= d_tau * d_kappa
# sometimes numerical difficulties arise as the solution is approached
# this loop tries to solve the equations using a sequence of functions
# for solve. For dense systems, the order is:
# 1. scipy.linalg.cho_factor/scipy.linalg.cho_solve,
# 2. scipy.linalg.solve w/ sym_pos = True,
# 3. scipy.linalg.solve w/ sym_pos = False, and if all else fails
# 4. scipy.linalg.lstsq
# For sparse systems, the order is:
# 1. scipy.sparse.linalg.splu
# 2. scipy.sparse.linalg.lsqr
# TODO: if umfpack is installed, use factorized instead of splu.
# Can't do that now because factorized doesn't pass permc_spec
# to splu if umfpack isn't installed. Also, umfpack not tested.
solved = False
while(not solved):
try:
solve_this = L if cholesky else M
# [1] Equation 8.28
p, q = _sym_solve(Dinv, solve_this, A, c, b, solve, splu)
# [1] Equation 8.29
u, v = _sym_solve(Dinv, solve_this, A, rhatd -
(1 / x) * rhatxs, rhatp, solve, splu)
if np.any(np.isnan(p)) or np.any(np.isnan(q)):
raise LinAlgError
solved = True
except (LinAlgError, ValueError) as e:
# Usually this doesn't happen. If it does, it happens when
# there are redundant constraints or when approaching the
# solution. If so, change solver.
cholesky = False
if not lstsq:
if sym_pos:
warn(
"Solving system with option 'sym_pos':True "
"failed. It is normal for this to happen "
"occasionally, especially as the solution is "
"approached. However, if you see this frequently, "
"consider setting option 'sym_pos' to False.",
OptimizeWarning)
sym_pos = False
else:
warn(
"Solving system with option 'sym_pos':False "
"failed. This may happen occasionally, "
"especially as the solution is "
"approached. However, if you see this frequently, "
"your problem may be numerically challenging. "
"If you cannot improve the formulation, consider "
"setting 'lstsq' to True. Consider also setting "
"`presolve` to True, if it is not already.",
OptimizeWarning)
lstsq = True
else:
raise e
solve = _get_solver(sparse, lstsq, sym_pos)
# [1] Results after 8.29
d_tau = ((rhatg + 1 / tau * rhattk - (-c.dot(u) + b.dot(v))) /
(1 / tau * kappa + (-c.dot(p) + b.dot(q))))
d_x = u + p * d_tau
d_y = v + q * d_tau
# [1] Relations between after 8.25 and 8.26
d_z = (1 / x) * (rhatxs - z * d_x)
d_kappa = 1 / tau * (rhattk - kappa * d_tau)
# [1] 8.12 and "Let alpha be the maximal possible step..." before 8.23
alpha = _get_step(x, d_x, z, d_z, tau, d_tau, kappa, d_kappa, 1)
if ip: # initial point - see [1] 4.4
gamma = 10
else: # predictor-corrector, [1] definition after 8.12
beta1 = 0.1 # [1] pg. 220 (Table 8.1)
gamma = (1 - alpha)**2 * min(beta1, (1 - alpha))
i += 1
return d_x, d_y, d_z, d_tau, d_kappa
def _sym_solve(Dinv, M, A, r1, r2, solve, splu=False):
"""
An implementation of [1] equation 8.31 and 8.32
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
"""
# [1] 8.31
r = r2 + A.dot(Dinv * r1)
if splu:
v = solve(r)
else:
v = solve(M, r)
# [1] 8.32
u = Dinv * (A.T.dot(v) - r1)
return u, v
def _get_step(x, d_x, z, d_z, tau, d_tau, kappa, d_kappa, alpha0):
"""
An implementation of [1] equation 8.21
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
"""
# [1] 4.3 Equation 8.21, ignoring 8.20 requirement
# same step is taken in primal and dual spaces
# alpha0 is basically beta3 from [1] Table 8.1, but instead of beta3
# the value 1 is used in Mehrota corrector and initial point correction
i_x = d_x < 0
i_z = d_z < 0
alpha_x = alpha0 * np.min(x[i_x] / -d_x[i_x]) if np.any(i_x) else 1
alpha_tau = alpha0 * tau / -d_tau if d_tau < 0 else 1
alpha_z = alpha0 * np.min(z[i_z] / -d_z[i_z]) if np.any(i_z) else 1
alpha_kappa = alpha0 * kappa / -d_kappa if d_kappa < 0 else 1
alpha = np.min([1, alpha_x, alpha_tau, alpha_z, alpha_kappa])
return alpha
def _get_message(status):
"""
Given problem status code, return a more detailed message.
Parameters
----------
status : int
An integer representing the exit status of the optimization::
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
4 : Serious numerical difficulties encountered.
Returns
-------
message : str
A string descriptor of the exit status of the optimization.
"""
messages = (
["Optimization terminated successfully.",
"The iteration limit was reached before the algorithm converged.",
"The algorithm terminated successfully and determined that the "
"problem is infeasible.",
"The algorithm terminated successfully and determined that the "
"problem is unbounded.",
"Numerical difficulties were encountered before the problem "
"converged. Please check your problem formulation for errors, "
"independence of linear equality constraints, and reasonable "
"scaling and matrix condition numbers. If you continue to "
"encounter this error, please submit a bug report."
])
return messages[status]
def _do_step(x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha):
"""
An implementation of [1] Equation 8.9
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
"""
x = x + alpha * d_x
tau = tau + alpha * d_tau
z = z + alpha * d_z
kappa = kappa + alpha * d_kappa
y = y + alpha * d_y
return x, y, z, tau, kappa
def _get_blind_start(shape):
"""
Return the starting point from [1] 4.4
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
"""
m, n = shape
x0 = np.ones(n)
y0 = np.zeros(m)
z0 = np.ones(n)
tau0 = 1
kappa0 = 1
return x0, y0, z0, tau0, kappa0
def _indicators(A, b, c, c0, x, y, z, tau, kappa):
"""
Implementation of several equations from [1] used as indicators of
the status of optimization.
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
"""
# residuals for termination are relative to initial values
x0, y0, z0, tau0, kappa0 = _get_blind_start(A.shape)
# See [1], Section 4 - The Homogeneous Algorithm, Equation 8.8
def r_p(x, tau):
return b * tau - A.dot(x)
def r_d(y, z, tau):
return c * tau - A.T.dot(y) - z
def r_g(x, y, kappa):
return kappa + c.dot(x) - b.dot(y)
# np.dot unpacks if they are arrays of size one
def mu(x, tau, z, kappa):
return (x.dot(z) + np.dot(tau, kappa)) / (len(x) + 1)
obj = c.dot(x / tau) + c0
def norm(a):
return np.linalg.norm(a)
# See [1], Section 4.5 - The Stopping Criteria
r_p0 = r_p(x0, tau0)
r_d0 = r_d(y0, z0, tau0)
r_g0 = r_g(x0, y0, kappa0)
mu_0 = mu(x0, tau0, z0, kappa0)
rho_A = norm(c.T.dot(x) - b.T.dot(y)) / (tau + norm(b.T.dot(y)))
rho_p = norm(r_p(x, tau)) / max(1, norm(r_p0))
rho_d = norm(r_d(y, z, tau)) / max(1, norm(r_d0))
rho_g = norm(r_g(x, y, kappa)) / max(1, norm(r_g0))
rho_mu = mu(x, tau, z, kappa) / mu_0
return rho_p, rho_d, rho_A, rho_g, rho_mu, obj
def _display_iter(rho_p, rho_d, rho_g, alpha, rho_mu, obj, header=False):
"""
Print indicators of optimization status to the console.
Parameters
----------
rho_p : float
The (normalized) primal feasibility, see [1] 4.5
rho_d : float
The (normalized) dual feasibility, see [1] 4.5
rho_g : float
The (normalized) duality gap, see [1] 4.5
alpha : float
The step size, see [1] 4.3
rho_mu : float
The (normalized) path parameter, see [1] 4.5
obj : float
The objective function value of the current iterate
header : bool
True if a header is to be printed
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
"""
if header:
print("Primal Feasibility ",
"Dual Feasibility ",
"Duality Gap ",
"Step ",
"Path Parameter ",
"Objective ")
# no clue why this works
fmt = '{0:<20.13}{1:<20.13}{2:<20.13}{3:<17.13}{4:<20.13}{5:<20.13}'
print(fmt.format(
rho_p,
rho_d,
rho_g,
alpha,
rho_mu,
obj))
def _ip_hsd(A, b, c, c0, alpha0, beta, maxiter, disp, tol,
sparse, lstsq, sym_pos, cholesky, pc, ip, permc_spec):
r"""
Solve a linear programming problem in standard form:
minimize: c'^T * x'
subject to: A * x' == b
0 < x' < oo
using the interior point method of [1].
Parameters
----------
A : 2-D array
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x`` (for standard form problem).
b : 1-D array
1-D array of values representing the RHS of each equality constraint
(row) in ``A`` (for standard form problem).
c : 1-D array
Coefficients of the linear objective function to be minimized (for
standard form problem).
c0 : float
Constant term in objective function due to fixed (and eliminated)
variables. (Purely for display.)
alpha0 : float
The maximal step size for Mehrota's predictor-corrector search
direction; see :math:`\beta_3`of [1] Table 8.1
beta : float
The desired reduction of the path parameter :math:`\mu` (see [3]_)
maxiter : int
The maximum number of iterations of the algorithm.
disp : bool
Set to ``True`` if indicators of optimization status are to be printed
to the console each iteration.
tol : float
Termination tolerance; see [1]_ Section 4.5.
sparse : bool
Set to ``True`` if the problem is to be treated as sparse. However,
the inputs ``A_eq`` and ``A_ub`` should nonetheless be provided as
(dense) arrays rather than sparse matrices.
lstsq : bool
Set to ``True`` if the problem is expected to be very poorly
conditioned. This should always be left as ``False`` unless severe
numerical difficulties are frequently encountered, and a better option
would be to improve the formulation of the problem.
sym_pos : bool
Leave ``True`` if the problem is expected to yield a well conditioned
symmetric positive definite normal equation matrix (almost always).
cholesky : bool
Set to ``True`` if the normal equations are to be solved by explicit
Cholesky decomposition followed by explicit forward/backward
substitution. This is typically faster for moderate, dense problems
that are numerically well-behaved.
pc : bool
Leave ``True`` if the predictor-corrector method of Mehrota is to be
used. This is almost always (if not always) beneficial.
ip : bool
Set to ``True`` if the improved initial point suggestion due to [1]_
Section 4.3 is desired. It's unclear whether this is beneficial.
permc_spec : str (default = 'MMD_AT_PLUS_A')
(Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos =
True``.) A matrix is factorized in each iteration of the algorithm.
This option specifies how to permute the columns of the matrix for
sparsity preservation. Acceptable values are:
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering.
This option can impact the convergence of the
interior point algorithm; test different values to determine which
performs best for your problem. For more information, refer to
``scipy.sparse.linalg.splu``.
Returns
-------
x_hat : float
Solution vector (for standard form problem).
status : int
An integer representing the exit status of the optimization::
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
4 : Serious numerical difficulties encountered.
message : str
A string descriptor of the exit status of the optimization.
iteration : int
The number of iterations taken to solve the problem
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
.. [3] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear
Programming based on Newton's Method." Unpublished Course Notes,
March 2004. Available 2/25/2017 at:
https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf
"""
iteration = 0
# default initial point
x, y, z, tau, kappa = _get_blind_start(A.shape)
# first iteration is special improvement of initial point
ip = ip if pc else False
# [1] 4.5
rho_p, rho_d, rho_A, rho_g, rho_mu, obj = _indicators(
A, b, c, c0, x, y, z, tau, kappa)
go = rho_p > tol or rho_d > tol or rho_A > tol # we might get lucky : )
if disp:
_display_iter(rho_p, rho_d, rho_g, "-", rho_mu, obj, header=True)
status = 0
message = "Optimization terminated successfully."
if sparse:
A = sps.csc_matrix(A)
A.T = A.transpose() # A.T is defined for sparse matrices but is slow
# Redefine it to avoid calculating again
# This is fine as long as A doesn't change
while go:
iteration += 1
if ip: # initial point
# [1] Section 4.4
gamma = 1
def eta(g):
return 1
else:
# gamma = 0 in predictor step according to [1] 4.1
# if predictor/corrector is off, use mean of complementarity [3]
# 5.1 / [4] Below Figure 10-4
gamma = 0 if pc else beta * np.mean(z * x)
# [1] Section 4.1
def eta(g=gamma):
return 1 - g
try:
# Solve [1] 8.6 and 8.7/8.13/8.23
d_x, d_y, d_z, d_tau, d_kappa = _get_delta(
A, b, c, x, y, z, tau, kappa, gamma, eta,
sparse, lstsq, sym_pos, cholesky, pc, ip, permc_spec)
if ip: # initial point
# [1] 4.4
# Formula after 8.23 takes a full step regardless if this will
# take it negative
alpha = 1.0
x, y, z, tau, kappa = _do_step(
x, y, z, tau, kappa, d_x, d_y,
d_z, d_tau, d_kappa, alpha)
x[x < 1] = 1
z[z < 1] = 1
tau = max(1, tau)
kappa = max(1, kappa)
ip = False # done with initial point
else:
# [1] Section 4.3
alpha = _get_step(x, d_x, z, d_z, tau,
d_tau, kappa, d_kappa, alpha0)
# [1] Equation 8.9
x, y, z, tau, kappa = _do_step(
x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha)
except (LinAlgError, FloatingPointError,
ValueError, ZeroDivisionError):
# this can happen when sparse solver is used and presolve
# is turned off. Also observed ValueError in AppVeyor Python 3.6
# Win32 build (PR #8676). I've never seen it otherwise.
status = 4
message = _get_message(status)
break
# [1] 4.5
rho_p, rho_d, rho_A, rho_g, rho_mu, obj = _indicators(
A, b, c, c0, x, y, z, tau, kappa)
go = rho_p > tol or rho_d > tol or rho_A > tol
if disp:
_display_iter(rho_p, rho_d, rho_g, alpha, float(rho_mu), obj)
# [1] 4.5
inf1 = (rho_p < tol and rho_d < tol and rho_g < tol and tau < tol *
max(1, kappa))
inf2 = rho_mu < tol and tau < tol * min(1, kappa)
if inf1 or inf2:
# [1] Lemma 8.4 / Theorem 8.3
if b.transpose().dot(y) > tol:
status = 2
else: # elif c.T.dot(x) < tol: ? Probably not necessary.
status = 3
message = _get_message(status)
break
elif iteration >= maxiter:
status = 1
message = _get_message(status)
break
if disp:
print(message)
x_hat = x / tau
# [1] Statement after Theorem 8.2
return x_hat, status, message, iteration
def _linprog_ip(
c,
A_ub=None,
b_ub=None,
A_eq=None,
b_eq=None,
bounds=None,
callback=None,
alpha0=.99995,
beta=0.1,
maxiter=1000,
disp=False,
tol=1e-8,
sparse=False,
lstsq=False,
sym_pos=True,
cholesky=None,
pc=True,
ip=False,
presolve=True,
permc_spec='MMD_AT_PLUS_A',
rr=True,
_sparse_presolve=False,
**unknown_options):
r"""
Minimize a linear objective function subject to linear
equality constraints, linear inequality constraints, and simple bounds
using the interior point method of [1]_.
Linear programming is intended to solve problems of the following form::
Minimize: c^T * x
Subject to: A_ub * x <= b_ub
A_eq * x == b_eq
bounds[i][0] < x_i < bounds[i][1]
Parameters
----------
c : array_like
Coefficients of the linear objective function to be minimized.
A_ub : array_like, optional
2-D array which, when matrix-multiplied by ``x``, gives the values of
the upper-bound inequality constraints at ``x``.
b_ub : array_like, optional
1-D array of values representing the upper-bound of each inequality
constraint (row) in ``A_ub``.
A_eq : array_like, optional
2-D array which, when matrix-multiplied by ``x``, gives the values of
the equality constraints at ``x``.
b_eq : array_like, optional
1-D array of values representing the right hand side of each equality
constraint (row) in ``A_eq``.
bounds : sequence, optional
``(min, max)`` pairs for each element in ``x``, defining
the bounds on that parameter. Use ``None`` for one of ``min`` or
``max`` when there is no bound in that direction. By default
bounds are ``(0, None)`` (non-negative).
If a sequence containing a single tuple is provided, then ``min`` and
``max`` will be applied to all variables in the problem.
Options
-------
maxiter : int (default = 1000)
The maximum number of iterations of the algorithm.
disp : bool (default = False)
Set to ``True`` if indicators of optimization status are to be printed
to the console each iteration.
tol : float (default = 1e-8)
Termination tolerance to be used for all termination criteria;
see [1]_ Section 4.5.
alpha0 : float (default = 0.99995)
The maximal step size for Mehrota's predictor-corrector search
direction; see :math:`\beta_{3}` of [1]_ Table 8.1.
beta : float (default = 0.1)
The desired reduction of the path parameter :math:`\mu` (see [3]_)
when Mehrota's predictor-corrector is not in use (uncommon).
sparse : bool (default = False)
Set to ``True`` if the problem is to be treated as sparse after
presolve. If either ``A_eq`` or ``A_ub`` is a sparse matrix,
this option will automatically be set ``True``, and the problem
will be treated as sparse even during presolve. If your constraint
matrices contain mostly zeros and the problem is not very small (less
than about 100 constraints or variables), consider setting ``True``
or providing ``A_eq`` and ``A_ub`` as sparse matrices.
lstsq : bool (default = False)
Set to ``True`` if the problem is expected to be very poorly
conditioned. This should always be left ``False`` unless severe
numerical difficulties are encountered. Leave this at the default
unless you receive a warning message suggesting otherwise.
sym_pos : bool (default = True)
Leave ``True`` if the problem is expected to yield a well conditioned
symmetric positive definite normal equation matrix
(almost always). Leave this at the default unless you receive
a warning message suggesting otherwise.
cholesky : bool (default = True)
Set to ``True`` if the normal equations are to be solved by explicit
Cholesky decomposition followed by explicit forward/backward
substitution. This is typically faster for moderate, dense problems
that are numerically well-behaved.
pc : bool (default = True)
Leave ``True`` if the predictor-corrector method of Mehrota is to be
used. This is almost always (if not always) beneficial.
ip : bool (default = False)
Set to ``True`` if the improved initial point suggestion due to [1]_
Section 4.3 is desired. Whether this is beneficial or not
depends on the problem.
presolve : bool (default = True)
Leave ``True`` if presolve routine should be run. The presolve routine
is almost always useful because it can detect trivial infeasibilities
and unboundedness, eliminate fixed variables, and remove redundancies.
One circumstance in which it might be turned off (set ``False``) is
when it detects that the problem is trivially unbounded; it is possible
that that the problem is truly infeasibile but this has not been
detected.
rr : bool (default = True)
Default ``True`` attempts to eliminate any redundant rows in ``A_eq``.
Set ``False`` if ``A_eq`` is known to be of full row rank, or if you
are looking for a potential speedup (at the expense of reliability).
permc_spec : str (default = 'MMD_AT_PLUS_A')
(Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos =
True``.) A matrix is factorized in each iteration of the algorithm.
This option specifies how to permute the columns of the matrix for
sparsity preservation. Acceptable values are:
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering.
This option can impact the convergence of the
interior point algorithm; test different values to determine which
performs best for your problem. For more information, refer to
``scipy.sparse.linalg.splu``.
Returns
-------
A ``scipy.optimize.OptimizeResult`` consisting of the following fields:
x : ndarray
The independent variable vector which optimizes the linear
programming problem.
fun : float
The optimal value of the objective function
con : float
The residuals of the equality constraints (nominally zero).
slack : ndarray
The values of the slack variables. Each slack variable corresponds
to an inequality constraint. If the slack is zero, then the
corresponding constraint is active.
success : bool
Returns True if the algorithm succeeded in finding an optimal
solution.
status : int
An integer representing the exit status of the optimization::
0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
4 : Serious numerical difficulties encountered
nit : int
The number of iterations performed.
message : str
A string descriptor of the exit status of the optimization.
Notes
-----
This method implements the algorithm outlined in [1]_ with ideas from [5]_
and a structure inspired by the simpler methods of [3]_ and [4]_.
First, a presolve procedure based on [5]_ attempts to identify trivial
infeasibilities, trivial unboundedness, and potential problem
simplifications. Specifically, it checks for:
- rows of zeros in ``A_eq`` or ``A_ub``, representing trivial constraints;
- columns of zeros in ``A_eq`` `and` ``A_ub``, representing unconstrained
variables;
- column singletons in ``A_eq``, representing fixed variables; and
- column singletons in ``A_ub``, representing simple bounds.
If presolve reveals that the problem is unbounded (e.g. an unconstrained
and unbounded variable has negative cost) or infeasible (e.g. a row of
zeros in ``A_eq`` corresponds with a nonzero in ``b_eq``), the solver
terminates with the appropriate status code. Note that presolve terminates
as soon as any sign of unboundedness is detected; consequently, a problem
may be reported as unbounded when in reality the problem is infeasible
(but infeasibility has not been detected yet). Therefore, if the output
message states that unboundedness is detected in presolve and it is
necessary to know whether the problem is actually infeasible, set option
``presolve=False``.
If neither infeasibility nor unboundedness are detected in a single pass
of the presolve check, bounds are tightened where possible and fixed
variables are removed from the problem. Then, linearly dependent rows
of the ``A_eq`` matrix are removed, (unless they represent an
infeasibility) to avoid numerical difficulties in the primary solve
routine. Note that rows that are nearly linearly dependent (within a
prescibed tolerance) may also be removed, which can change the optimal
solution in rare cases. If this is a concern, eliminate redundancy from
your problem formulation and run with option ``rr=False`` or
``presolve=False``.
Several potential improvements can be made here: additional presolve
checks outlined in [5]_ should be implemented, the presolve routine should
be run multiple times (until no further simplifications can be made), and
more of the efficiency improvements from [2]_ should be implemented in the
redundancy removal routines.
After presolve, the problem is transformed to standard form by converting
the (tightened) simple bounds to upper bound constraints, introducing
non-negative slack variables for inequality constraints, and expressing
unbounded variables as the difference between two non-negative variables.
The primal-dual path following method begins with initial 'guesses' of
the primal and dual variables of the standard form problem and iteratively
attempts to solve the (nonlinear) Karush-Kuhn-Tucker conditions for the
problem with a gradually reduced logarithmic barrier term added to the
objective. This particular implementation uses a homogeneous self-dual
formulation, which provides certificates of infeasibility or unboundedness
where applicable.
The default initial point for the primal and dual variables is that
defined in [1]_ Section 4.4 Equation 8.22. Optionally (by setting initial
point option ``ip=True``), an alternate (potentially improved) starting
point can be calculated according to the additional recommendations of
[1]_ Section 4.4.
A search direction is calculated using the predictor-corrector method
(single correction) proposed by Mehrota and detailed in [1]_ Section 4.1.
(A potential improvement would be to implement the method of multiple
corrections described in [1]_ Section 4.2.) In practice, this is
accomplished by solving the normal equations, [1]_ Section 5.1 Equations
8.31 and 8.32, derived from the Newton equations [1]_ Section 5 Equations
8.25 (compare to [1]_ Section 4 Equations 8.6-8.8). The advantage of
solving the normal equations rather than 8.25 directly is that the
matrices involved are symmetric positive definite, so Cholesky
decomposition can be used rather than the more expensive LU factorization.
With the default ``cholesky=True``, this is accomplished using
``scipy.linalg.cho_factor`` followed by forward/backward substitutions
via ``scipy.linalg.cho_solve``. With ``cholesky=False`` and
``sym_pos=True``, Cholesky decomposition is performed instead by
``scipy.linalg.solve``. Based on speed tests, this also appears to retain
the Cholesky decomposition of the matrix for later use, which is beneficial
as the same system is solved four times with different right hand sides
in each iteration of the algorithm.
In problems with redundancy (e.g. if presolve is turned off with option
``presolve=False``) or if the matrices become ill-conditioned (e.g. as the
solution is approached and some decision variables approach zero),
Cholesky decomposition can fail. Should this occur, successively more
robust solvers (``scipy.linalg.solve`` with ``sym_pos=False`` then
``scipy.linalg.lstsq``) are tried, at the cost of computational efficiency.
These solvers can be used from the outset by setting the options
``sym_pos=False`` and ``lstsq=True``, respectively.
Note that with the option ``sparse=True``, the normal equations are solved
using ``scipy.sparse.linalg.spsolve``. Unfortunately, this uses the more
expensive LU decomposition from the outset, but for large, sparse problems,
the use of sparse linear algebra techniques improves the solve speed
despite the use of LU rather than Cholesky decomposition. A simple
improvement would be to use the sparse Cholesky decomposition of
``CHOLMOD`` via ``scikit-sparse`` when available.
Other potential improvements for combatting issues associated with dense
columns in otherwise sparse problems are outlined in [1]_ Section 5.3 and
[7]_ Section 4.1-4.2; the latter also discusses the alleviation of
accuracy issues associated with the substitution approach to free
variables.
After calculating the search direction, the maximum possible step size
that does not activate the non-negativity constraints is calculated, and
the smaller of this step size and unity is applied (as in [1]_ Section
4.1.) [1]_ Section 4.3 suggests improvements for choosing the step size.
The new point is tested according to the termination conditions of [1]_
Section 4.5. The same tolerance, which can be set using the ``tol`` option,
is used for all checks. (A potential improvement would be to expose
the different tolerances to be set independently.) If optimality,
unboundedness, or infeasibility is detected, the solve procedure
terminates; otherwise it repeats.
If optimality is achieved, a postsolve procedure undoes transformations
associated with presolve and converting to standard form. It then
calculates the residuals (equality constraint violations, which should
be very small) and slacks (difference between the left and right hand
sides of the upper bound constraints) of the original problem, which are
returned with the solution in an ``OptimizeResult`` object.
References
----------
.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
optimizer for linear programming: an implementation of the
homogeneous algorithm." High performance optimization. Springer US,
2000. 197-232.
.. [2] Andersen, Erling D. "Finding all linearly dependent rows in
large-scale linear programming." Optimization Methods and Software
6.3 (1995): 219-227.
.. [3] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear
Programming based on Newton's Method." Unpublished Course Notes,
March 2004. Available 2/25/2017 at
https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf
.. [4] Fourer, Robert. "Solving Linear Programs by Interior-Point Methods."
Unpublished Course Notes, August 26, 2005. Available 2/25/2017 at
http://www.4er.org/CourseNotes/Book%20B/B-III.pdf
.. [5] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear
programming." Mathematical Programming 71.2 (1995): 221-245.
.. [6] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear
programming." Athena Scientific 1 (1997): 997.
.. [7] Andersen, Erling D., et al. Implementation of interior point methods
for large scale linear programming. HEC/Universite de Geneve, 1996.
"""
_check_unknown_options(unknown_options)
if callback is not None:
raise NotImplementedError("method 'interior-point' does not support "
"callback functions.")
# This is an undocumented option for unit testing sparse presolve
if _sparse_presolve and A_eq is not None:
A_eq = sp.sparse.coo_matrix(A_eq)
if _sparse_presolve and A_ub is not None:
A_ub = sp.sparse.coo_matrix(A_ub)
# These should be warnings, not errors
if not sparse and (sp.sparse.issparse(A_eq) or sp.sparse.issparse(A_ub)):
sparse = True
warn("Sparse constraint matrix detected; setting 'sparse':True.",
OptimizeWarning)
if sparse and lstsq:
warn("Invalid option combination 'sparse':True "
"and 'lstsq':True; Sparse least squares is not recommended.",
OptimizeWarning)
if sparse and not sym_pos:
warn("Invalid option combination 'sparse':True "
"and 'sym_pos':False; the effect is the same as sparse least "
"squares, which is not recommended.",
OptimizeWarning)
if sparse and cholesky:
# Cholesky decomposition is not available for sparse problems
warn("Invalid option combination 'sparse':True "
"and 'cholesky':True; sparse Colesky decomposition is not "
"available.",
OptimizeWarning)
if lstsq and cholesky:
warn("Invalid option combination 'lstsq':True "
"and 'cholesky':True; option 'cholesky' has no effect when "
"'lstsq' is set True.",
OptimizeWarning)
valid_permc_spec = ('NATURAL', 'MMD_ATA', 'MMD_AT_PLUS_A', 'COLAMD')
if permc_spec.upper() not in valid_permc_spec:
warn("Invalid permc_spec option: '" + str(permc_spec) + "'. "
"Acceptable values are 'NATURAL', 'MMD_ATA', 'MMD_AT_PLUS_A', "
"and 'COLAMD'. Reverting to default.",
OptimizeWarning)
permc_spec = 'MMD_AT_PLUS_A'
# This can be an error
if not sym_pos and cholesky:
raise ValueError(
"Invalid option combination 'sym_pos':False "
"and 'cholesky':True: Cholesky decomposition is only possible "
"for symmetric positive definite matrices.")
cholesky = cholesky is None and sym_pos and not sparse and not lstsq
iteration = 0
complete = False # will become True if solved in presolve
undo = []
# Convert lists to numpy arrays, etc...
c, A_ub, b_ub, A_eq, b_eq, bounds = _clean_inputs(
c, A_ub, b_ub, A_eq, b_eq, bounds)
# Keep the original arrays to calculate slack/residuals for original
# problem.
c_o, A_ub_o, b_ub_o, A_eq_o, b_eq_o = c.copy(
), A_ub.copy(), b_ub.copy(), A_eq.copy(), b_eq.copy()
# Solve trivial problem, eliminate variables, tighten bounds, etc...
c0 = 0 # we might get a constant term in the objective
if presolve is True:
(c, c0, A_ub, b_ub, A_eq, b_eq, bounds, x, undo, complete, status,
message) = _presolve(c, A_ub, b_ub, A_eq, b_eq, bounds, rr)
# If not solved in presolve, solve it
if not complete:
# Convert problem to standard form
A, b, c, c0 = _get_Abc(c, c0, A_ub, b_ub, A_eq, b_eq, bounds, undo)
# Solve the problem
x, status, message, iteration = _ip_hsd(A, b, c, c0, alpha0, beta,
maxiter, disp, tol, sparse,
lstsq, sym_pos, cholesky,
pc, ip, permc_spec)
# Eliminate artificial variables, re-introduce presolved variables, etc...
# need modified bounds here to translate variables appropriately
x, fun, slack, con, status, message = _postprocess(
x, c_o, A_ub_o, b_ub_o, A_eq_o, b_eq_o,
bounds, complete, undo, status, message, tol)
sol = {
'x': x,
'fun': fun,
'slack': slack,
'con': con,
'status': status,
'message': message,
'nit': iteration,
"success": status == 0}
return OptimizeResult(sol)
| 89,346 | 40.192716 | 143 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_differentiable_functions.py
|
from __future__ import division, print_function, absolute_import
import numpy as np
import scipy.sparse as sps
from ._numdiff import approx_derivative, group_columns
from ._hessian_update_strategy import HessianUpdateStrategy
from scipy.sparse.linalg import LinearOperator
from copy import deepcopy
FD_METHODS = ('2-point', '3-point', 'cs')
class ScalarFunction(object):
"""Scalar function and its derivatives.
This class defines a scalar function F: R^n->R and methods for
computing or approximating its first and second derivatives.
Notes
-----
This class implements a memoization logic. There are methods `fun`,
`grad`, hess` and corresponding attributes `f`, `g` and `H`. The following
things should be considered:
1. Use only public methods `fun`, `grad` and `hess`.
2. After one of the methods is called, the corresponding attribute
will be set. However, a subsequent call with a different argument
of *any* of the methods may overwrite the attribute.
"""
def __init__(self, fun, x0, args, grad, hess, finite_diff_rel_step,
finite_diff_bounds):
if not callable(grad) and grad not in FD_METHODS:
raise ValueError("`grad` must be either callable or one of {}."
.format(FD_METHODS))
if not (callable(hess) or hess in FD_METHODS
or isinstance(hess, HessianUpdateStrategy)):
raise ValueError("`hess` must be either callable,"
"HessianUpdateStrategy or one of {}."
.format(FD_METHODS))
if grad in FD_METHODS and hess in FD_METHODS:
raise ValueError("Whenever the gradient is estimated via "
"finite-differences, we require the Hessian "
"to be estimated using one of the "
"quasi-Newton strategies.")
self.x = np.atleast_1d(x0).astype(float)
self.n = self.x.size
self.nfev = 0
self.ngev = 0
self.nhev = 0
self.f_updated = False
self.g_updated = False
self.H_updated = False
finite_diff_options = {}
if grad in FD_METHODS:
finite_diff_options["method"] = grad
finite_diff_options["rel_step"] = finite_diff_rel_step
finite_diff_options["bounds"] = finite_diff_bounds
if hess in FD_METHODS:
finite_diff_options["method"] = hess
finite_diff_options["rel_step"] = finite_diff_rel_step
finite_diff_options["as_linear_operator"] = True
# Function evaluation
def fun_wrapped(x):
self.nfev += 1
return fun(x, *args)
def update_fun():
self.f = fun_wrapped(self.x)
self._update_fun_impl = update_fun
self._update_fun()
# Gradient evaluation
if callable(grad):
def grad_wrapped(x):
self.ngev += 1
return np.atleast_1d(grad(x, *args))
def update_grad():
self.g = grad_wrapped(self.x)
elif grad in FD_METHODS:
def update_grad():
self._update_fun()
self.g = approx_derivative(fun_wrapped, self.x, f0=self.f,
**finite_diff_options)
self._update_grad_impl = update_grad
self._update_grad()
# Hessian Evaluation
if callable(hess):
self.H = hess(x0, *args)
self.H_updated = True
self.nhev += 1
if sps.issparse(self.H):
def hess_wrapped(x):
self.nhev += 1
return sps.csr_matrix(hess(x, *args))
self.H = sps.csr_matrix(self.H)
elif isinstance(self.H, LinearOperator):
def hess_wrapped(x):
self.nhev += 1
return hess(x, *args)
else:
def hess_wrapped(x):
self.nhev += 1
return np.atleast_2d(np.asarray(hess(x, *args)))
self.H = np.atleast_2d(np.asarray(self.H))
def update_hess():
self.H = hess_wrapped(self.x)
elif hess in FD_METHODS:
def update_hess():
self._update_grad()
self.H = approx_derivative(grad_wrapped, self.x, f0=self.g,
**finite_diff_options)
return self.H
update_hess()
self.H_updated = True
elif isinstance(hess, HessianUpdateStrategy):
self.H = hess
self.H.initialize(self.n, 'hess')
self.H_updated = True
self.x_prev = None
self.g_prev = None
def update_hess():
self._update_grad()
self.H.update(self.x - self.x_prev, self.g - self.g_prev)
self._update_hess_impl = update_hess
if isinstance(hess, HessianUpdateStrategy):
def update_x(x):
self._update_grad()
self.x_prev = self.x
self.g_prev = self.g
self.x = x
self.f_updated = False
self.g_updated = False
self.H_updated = False
self._update_hess()
else:
def update_x(x):
self.x = x
self.f_updated = False
self.g_updated = False
self.H_updated = False
self._update_x_impl = update_x
def _update_fun(self):
if not self.f_updated:
self._update_fun_impl()
self.f_updated = True
def _update_grad(self):
if not self.g_updated:
self._update_grad_impl()
self.g_updated = True
def _update_hess(self):
if not self.H_updated:
self._update_hess_impl()
self.H_updated = True
def fun(self, x):
if not np.array_equal(x, self.x):
self._update_x_impl(x)
self._update_fun()
return self.f
def grad(self, x):
if not np.array_equal(x, self.x):
self._update_x_impl(x)
self._update_grad()
return self.g
def hess(self, x):
if not np.array_equal(x, self.x):
self._update_x_impl(x)
self._update_hess()
return self.H
class VectorFunction(object):
"""Vector function and its derivatives.
This class defines a vector function F: R^n->R^m and methods for
computing or approximating its first and second derivatives.
Notes
-----
This class implements a memoization logic. There are methods `fun`,
`jac`, hess` and corresponding attributes `f`, `J` and `H`. The following
things should be considered:
1. Use only public methods `fun`, `jac` and `hess`.
2. After one of the methods is called, the corresponding attribute
will be set. However, a subsequent call with a different argument
of *any* of the methods may overwrite the attribute.
"""
def __init__(self, fun, x0, jac, hess,
finite_diff_rel_step, finite_diff_jac_sparsity,
finite_diff_bounds, sparse_jacobian):
if not callable(jac) and jac not in FD_METHODS:
raise ValueError("`jac` must be either callable or one of {}."
.format(FD_METHODS))
if not (callable(hess) or hess in FD_METHODS
or isinstance(hess, HessianUpdateStrategy)):
raise ValueError("`hess` must be either callable,"
"HessianUpdateStrategy or one of {}."
.format(FD_METHODS))
if jac in FD_METHODS and hess in FD_METHODS:
raise ValueError("Whenever the Jacobian is estimated via "
"finite-differences, we require the Hessian to "
"be estimated using one of the quasi-Newton "
"strategies.")
self.x = np.atleast_1d(x0).astype(float)
self.n = self.x.size
self.nfev = 0
self.njev = 0
self.nhev = 0
self.f_updated = False
self.J_updated = False
self.H_updated = False
finite_diff_options = {}
if jac in FD_METHODS:
finite_diff_options["method"] = jac
finite_diff_options["rel_step"] = finite_diff_rel_step
if finite_diff_jac_sparsity is not None:
sparsity_groups = group_columns(finite_diff_jac_sparsity)
finite_diff_options["sparsity"] = (finite_diff_jac_sparsity,
sparsity_groups)
finite_diff_options["bounds"] = finite_diff_bounds
self.x_diff = np.copy(self.x)
if hess in FD_METHODS:
finite_diff_options["method"] = hess
finite_diff_options["rel_step"] = finite_diff_rel_step
finite_diff_options["as_linear_operator"] = True
self.x_diff = np.copy(self.x)
if jac in FD_METHODS and hess in FD_METHODS:
raise ValueError("Whenever the Jacobian is estimated via "
"finite-differences, we require the Hessian to "
"be estimated using one of the quasi-Newton "
"strategies.")
# Function evaluation
def fun_wrapped(x):
self.nfev += 1
return np.atleast_1d(fun(x))
def update_fun():
self.f = fun_wrapped(self.x)
self._update_fun_impl = update_fun
update_fun()
self.v = np.zeros_like(self.f)
self.m = self.v.size
# Jacobian Evaluation
if callable(jac):
self.J = jac(self.x)
self.J_updated = True
self.njev += 1
if (sparse_jacobian or
sparse_jacobian is None and sps.issparse(self.J)):
def jac_wrapped(x):
self.njev += 1
return sps.csr_matrix(jac(x))
self.J = sps.csr_matrix(self.J)
self.sparse_jacobian = True
elif sps.issparse(self.J):
def jac_wrapped(x):
self.njev += 1
return jac(x).toarray()
self.J = self.J.toarray()
self.sparse_jacobian = False
else:
def jac_wrapped(x):
self.njev += 1
return np.atleast_2d(jac(x))
self.J = np.atleast_2d(self.J)
self.sparse_jacobian = False
def update_jac():
self.J = jac_wrapped(self.x)
elif jac in FD_METHODS:
self.J = approx_derivative(fun_wrapped, self.x, f0=self.f,
**finite_diff_options)
self.J_updated = True
if (sparse_jacobian or
sparse_jacobian is None and sps.issparse(self.J)):
def update_jac():
self._update_fun()
self.J = sps.csr_matrix(
approx_derivative(fun_wrapped, self.x, f0=self.f,
**finite_diff_options))
self.J = sps.csr_matrix(self.J)
self.sparse_jacobian = True
elif sps.issparse(self.J):
def update_jac():
self._update_fun()
self.J = approx_derivative(fun_wrapped, self.x, f0=self.f,
**finite_diff_options).toarray()
self.J = self.J.toarray()
self.sparse_jacobian = False
else:
def update_jac():
self._update_fun()
self.J = np.atleast_2d(
approx_derivative(fun_wrapped, self.x, f0=self.f,
**finite_diff_options))
self.J = np.atleast_2d(self.J)
self.sparse_jacobian = False
self._update_jac_impl = update_jac
# Define Hessian
if callable(hess):
self.H = hess(self.x, self.v)
self.H_updated = True
self.nhev += 1
if sps.issparse(self.H):
def hess_wrapped(x, v):
self.nhev += 1
return sps.csr_matrix(hess(x, v))
self.H = sps.csr_matrix(self.H)
elif isinstance(self.H, LinearOperator):
def hess_wrapped(x, v):
self.nhev += 1
return hess(x, v)
else:
def hess_wrapped(x, v):
self.nhev += 1
return np.atleast_2d(np.asarray(hess(x, v)))
self.H = np.atleast_2d(np.asarray(self.H))
def update_hess():
self.H = hess_wrapped(self.x, self.v)
elif hess in FD_METHODS:
def jac_dot_v(x, v):
return jac_wrapped(x).T.dot(v)
def update_hess():
self._update_jac()
self.H = approx_derivative(jac_dot_v, self.x,
f0=self.J.T.dot(self.v),
args=(self.v,),
**finite_diff_options)
update_hess()
self.H_updated = True
elif isinstance(hess, HessianUpdateStrategy):
self.H = hess
self.H.initialize(self.n, 'hess')
self.H_updated = True
self.x_prev = None
self.J_prev = None
def update_hess():
self._update_jac()
# When v is updated before x was updated, then x_prev and
# J_prev are None and we need this check.
if self.x_prev is not None and self.J_prev is not None:
delta_x = self.x - self.x_prev
delta_g = self.J.T.dot(self.v) - self.J_prev.T.dot(self.v)
self.H.update(delta_x, delta_g)
self._update_hess_impl = update_hess
if isinstance(hess, HessianUpdateStrategy):
def update_x(x):
self._update_jac()
self.x_prev = self.x
self.J_prev = self.J
self.x = x
self.f_updated = False
self.J_updated = False
self.H_updated = False
self._update_hess()
else:
def update_x(x):
self.x = x
self.f_updated = False
self.J_updated = False
self.H_updated = False
self._update_x_impl = update_x
def _update_v(self, v):
if not np.array_equal(v, self.v):
self.v = v
self.H_updated = False
def _update_x(self, x):
if not np.array_equal(x, self.x):
self._update_x_impl(x)
def _update_fun(self):
if not self.f_updated:
self._update_fun_impl()
self.f_updated = True
def _update_jac(self):
if not self.J_updated:
self._update_jac_impl()
self.J_updated = True
def _update_hess(self):
if not self.H_updated:
self._update_hess_impl()
self.H_updated = True
def fun(self, x):
self._update_x(x)
self._update_fun()
return self.f
def jac(self, x):
self._update_x(x)
self._update_jac()
return self.J
def hess(self, x, v):
# v should be updated before x.
self._update_v(v)
self._update_x(x)
self._update_hess()
return self.H
class LinearVectorFunction(object):
"""Linear vector function and its derivatives.
Defines a linear function F = A x, where x is n-dimensional vector and
A is m-by-n matrix. The Jacobian is constant and equals to A. The Hessian
is identically zero and it is returned as a csr matrix.
"""
def __init__(self, A, x0, sparse_jacobian):
if sparse_jacobian or sparse_jacobian is None and sps.issparse(A):
self.J = sps.csr_matrix(A)
self.sparse_jacobian = True
elif sps.issparse(A):
self.J = A.toarray()
self.sparse_jacobian = False
else:
self.J = np.atleast_2d(A)
self.sparse_jacobian = False
self.m, self.n = self.J.shape
self.x = np.atleast_1d(x0).astype(float)
self.f = self.J.dot(self.x)
self.f_updated = True
self.v = np.zeros(self.m, dtype=float)
self.H = sps.csr_matrix((self.n, self.n))
def _update_x(self, x):
if not np.array_equal(x, self.x):
self.x = x
self.f_updated = False
def fun(self, x):
self._update_x(x)
if not self.f_updated:
self.f = self.J.dot(x)
self.f_updated = True
return self.f
def jac(self, x):
self._update_x(x)
return self.J
def hess(self, x, v):
self._update_x(x)
self.v = v
return self.H
class IdentityVectorFunction(LinearVectorFunction):
"""Identity vector function and its derivatives.
The Jacobian is the identity matrix, returned as a dense array when
`sparse_jacobian=False` and as a csr matrix otherwise. The Hessian is
identically zero and it is returned as a csr matrix.
"""
def __init__(self, x0, sparse_jacobian):
n = len(x0)
if sparse_jacobian or sparse_jacobian is None:
A = sps.eye(n, format='csr')
sparse_jacobian = True
else:
A = np.eye(n)
sparse_jacobian = False
super(IdentityVectorFunction, self).__init__(A, x0, sparse_jacobian)
| 18,036 | 33.487572 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/linesearch.py
|
"""
Functions
---------
.. autosummary::
:toctree: generated/
line_search_armijo
line_search_wolfe1
line_search_wolfe2
scalar_search_wolfe1
scalar_search_wolfe2
"""
from __future__ import division, print_function, absolute_import
from warnings import warn
from scipy.optimize import minpack2
import numpy as np
from scipy._lib.six import xrange
__all__ = ['LineSearchWarning', 'line_search_wolfe1', 'line_search_wolfe2',
'scalar_search_wolfe1', 'scalar_search_wolfe2',
'line_search_armijo']
class LineSearchWarning(RuntimeWarning):
pass
#------------------------------------------------------------------------------
# Minpack's Wolfe line and scalar searches
#------------------------------------------------------------------------------
def line_search_wolfe1(f, fprime, xk, pk, gfk=None,
old_fval=None, old_old_fval=None,
args=(), c1=1e-4, c2=0.9, amax=50, amin=1e-8,
xtol=1e-14):
"""
As `scalar_search_wolfe1` but do a line search to direction `pk`
Parameters
----------
f : callable
Function `f(x)`
fprime : callable
Gradient of `f`
xk : array_like
Current point
pk : array_like
Search direction
gfk : array_like, optional
Gradient of `f` at point `xk`
old_fval : float, optional
Value of `f` at point `xk`
old_old_fval : float, optional
Value of `f` at point preceding `xk`
The rest of the parameters are the same as for `scalar_search_wolfe1`.
Returns
-------
stp, f_count, g_count, fval, old_fval
As in `line_search_wolfe1`
gval : array
Gradient of `f` at the final point
"""
if gfk is None:
gfk = fprime(xk)
if isinstance(fprime, tuple):
eps = fprime[1]
fprime = fprime[0]
newargs = (f, eps) + args
gradient = False
else:
newargs = args
gradient = True
gval = [gfk]
gc = [0]
fc = [0]
def phi(s):
fc[0] += 1
return f(xk + s*pk, *args)
def derphi(s):
gval[0] = fprime(xk + s*pk, *newargs)
if gradient:
gc[0] += 1
else:
fc[0] += len(xk) + 1
return np.dot(gval[0], pk)
derphi0 = np.dot(gfk, pk)
stp, fval, old_fval = scalar_search_wolfe1(
phi, derphi, old_fval, old_old_fval, derphi0,
c1=c1, c2=c2, amax=amax, amin=amin, xtol=xtol)
return stp, fc[0], gc[0], fval, old_fval, gval[0]
def scalar_search_wolfe1(phi, derphi, phi0=None, old_phi0=None, derphi0=None,
c1=1e-4, c2=0.9,
amax=50, amin=1e-8, xtol=1e-14):
"""
Scalar function search for alpha that satisfies strong Wolfe conditions
alpha > 0 is assumed to be a descent direction.
Parameters
----------
phi : callable phi(alpha)
Function at point `alpha`
derphi : callable dphi(alpha)
Derivative `d phi(alpha)/ds`. Returns a scalar.
phi0 : float, optional
Value of `f` at 0
old_phi0 : float, optional
Value of `f` at the previous point
derphi0 : float, optional
Value `derphi` at 0
c1, c2 : float, optional
Wolfe parameters
amax, amin : float, optional
Maximum and minimum step size
xtol : float, optional
Relative tolerance for an acceptable step.
Returns
-------
alpha : float
Step size, or None if no suitable step was found
phi : float
Value of `phi` at the new point `alpha`
phi0 : float
Value of `phi` at `alpha=0`
Notes
-----
Uses routine DCSRCH from MINPACK.
"""
if phi0 is None:
phi0 = phi(0.)
if derphi0 is None:
derphi0 = derphi(0.)
if old_phi0 is not None and derphi0 != 0:
alpha1 = min(1.0, 1.01*2*(phi0 - old_phi0)/derphi0)
if alpha1 < 0:
alpha1 = 1.0
else:
alpha1 = 1.0
phi1 = phi0
derphi1 = derphi0
isave = np.zeros((2,), np.intc)
dsave = np.zeros((13,), float)
task = b'START'
maxiter = 100
for i in xrange(maxiter):
stp, phi1, derphi1, task = minpack2.dcsrch(alpha1, phi1, derphi1,
c1, c2, xtol, task,
amin, amax, isave, dsave)
if task[:2] == b'FG':
alpha1 = stp
phi1 = phi(stp)
derphi1 = derphi(stp)
else:
break
else:
# maxiter reached, the line search did not converge
stp = None
if task[:5] == b'ERROR' or task[:4] == b'WARN':
stp = None # failed
return stp, phi1, phi0
line_search = line_search_wolfe1
#------------------------------------------------------------------------------
# Pure-Python Wolfe line and scalar searches
#------------------------------------------------------------------------------
def line_search_wolfe2(f, myfprime, xk, pk, gfk=None, old_fval=None,
old_old_fval=None, args=(), c1=1e-4, c2=0.9, amax=None,
extra_condition=None, maxiter=10):
"""Find alpha that satisfies strong Wolfe conditions.
Parameters
----------
f : callable f(x,*args)
Objective function.
myfprime : callable f'(x,*args)
Objective function gradient.
xk : ndarray
Starting point.
pk : ndarray
Search direction.
gfk : ndarray, optional
Gradient value for x=xk (xk being the current parameter
estimate). Will be recomputed if omitted.
old_fval : float, optional
Function value for x=xk. Will be recomputed if omitted.
old_old_fval : float, optional
Function value for the point preceding x=xk
args : tuple, optional
Additional arguments passed to objective function.
c1 : float, optional
Parameter for Armijo condition rule.
c2 : float, optional
Parameter for curvature condition rule.
amax : float, optional
Maximum step size
extra_condition : callable, optional
A callable of the form ``extra_condition(alpha, x, f, g)``
returning a boolean. Arguments are the proposed step ``alpha``
and the corresponding ``x``, ``f`` and ``g`` values. The line search
accepts the value of ``alpha`` only if this
callable returns ``True``. If the callable returns ``False``
for the step length, the algorithm will continue with
new iterates. The callable is only called for iterates
satisfying the strong Wolfe conditions.
maxiter : int, optional
Maximum number of iterations to perform
Returns
-------
alpha : float or None
Alpha for which ``x_new = x0 + alpha * pk``,
or None if the line search algorithm did not converge.
fc : int
Number of function evaluations made.
gc : int
Number of gradient evaluations made.
new_fval : float or None
New function value ``f(x_new)=f(x0+alpha*pk)``,
or None if the line search algorithm did not converge.
old_fval : float
Old function value ``f(x0)``.
new_slope : float or None
The local slope along the search direction at the
new value ``<myfprime(x_new), pk>``,
or None if the line search algorithm did not converge.
Notes
-----
Uses the line search algorithm to enforce strong Wolfe
conditions. See Wright and Nocedal, 'Numerical Optimization',
1999, pg. 59-60.
For the zoom phase it uses an algorithm by [...].
"""
fc = [0]
gc = [0]
gval = [None]
gval_alpha = [None]
def phi(alpha):
fc[0] += 1
return f(xk + alpha * pk, *args)
if isinstance(myfprime, tuple):
def derphi(alpha):
fc[0] += len(xk) + 1
eps = myfprime[1]
fprime = myfprime[0]
newargs = (f, eps) + args
gval[0] = fprime(xk + alpha * pk, *newargs) # store for later use
gval_alpha[0] = alpha
return np.dot(gval[0], pk)
else:
fprime = myfprime
def derphi(alpha):
gc[0] += 1
gval[0] = fprime(xk + alpha * pk, *args) # store for later use
gval_alpha[0] = alpha
return np.dot(gval[0], pk)
if gfk is None:
gfk = fprime(xk, *args)
derphi0 = np.dot(gfk, pk)
if extra_condition is not None:
# Add the current gradient as argument, to avoid needless
# re-evaluation
def extra_condition2(alpha, phi):
if gval_alpha[0] != alpha:
derphi(alpha)
x = xk + alpha * pk
return extra_condition(alpha, x, phi, gval[0])
else:
extra_condition2 = None
alpha_star, phi_star, old_fval, derphi_star = scalar_search_wolfe2(
phi, derphi, old_fval, old_old_fval, derphi0, c1, c2, amax,
extra_condition2, maxiter=maxiter)
if derphi_star is None:
warn('The line search algorithm did not converge', LineSearchWarning)
else:
# derphi_star is a number (derphi) -- so use the most recently
# calculated gradient used in computing it derphi = gfk*pk
# this is the gradient at the next step no need to compute it
# again in the outer loop.
derphi_star = gval[0]
return alpha_star, fc[0], gc[0], phi_star, old_fval, derphi_star
def scalar_search_wolfe2(phi, derphi=None, phi0=None,
old_phi0=None, derphi0=None,
c1=1e-4, c2=0.9, amax=None,
extra_condition=None, maxiter=10):
"""Find alpha that satisfies strong Wolfe conditions.
alpha > 0 is assumed to be a descent direction.
Parameters
----------
phi : callable f(x)
Objective scalar function.
derphi : callable f'(x), optional
Objective function derivative (can be None)
phi0 : float, optional
Value of phi at s=0
old_phi0 : float, optional
Value of phi at previous point
derphi0 : float, optional
Value of derphi at s=0
c1 : float, optional
Parameter for Armijo condition rule.
c2 : float, optional
Parameter for curvature condition rule.
amax : float, optional
Maximum step size
extra_condition : callable, optional
A callable of the form ``extra_condition(alpha, phi_value)``
returning a boolean. The line search accepts the value
of ``alpha`` only if this callable returns ``True``.
If the callable returns ``False`` for the step length,
the algorithm will continue with new iterates.
The callable is only called for iterates satisfying
the strong Wolfe conditions.
maxiter : int, optional
Maximum number of iterations to perform
Returns
-------
alpha_star : float or None
Best alpha, or None if the line search algorithm did not converge.
phi_star : float
phi at alpha_star
phi0 : float
phi at 0
derphi_star : float or None
derphi at alpha_star, or None if the line search algorithm
did not converge.
Notes
-----
Uses the line search algorithm to enforce strong Wolfe
conditions. See Wright and Nocedal, 'Numerical Optimization',
1999, pg. 59-60.
For the zoom phase it uses an algorithm by [...].
"""
if phi0 is None:
phi0 = phi(0.)
if derphi0 is None and derphi is not None:
derphi0 = derphi(0.)
alpha0 = 0
if old_phi0 is not None and derphi0 != 0:
alpha1 = min(1.0, 1.01*2*(phi0 - old_phi0)/derphi0)
else:
alpha1 = 1.0
if alpha1 < 0:
alpha1 = 1.0
phi_a1 = phi(alpha1)
#derphi_a1 = derphi(alpha1) evaluated below
phi_a0 = phi0
derphi_a0 = derphi0
if extra_condition is None:
extra_condition = lambda alpha, phi: True
for i in xrange(maxiter):
if alpha1 == 0 or (amax is not None and alpha0 == amax):
# alpha1 == 0: This shouldn't happen. Perhaps the increment has
# slipped below machine precision?
alpha_star = None
phi_star = phi0
phi0 = old_phi0
derphi_star = None
if alpha1 == 0:
msg = 'Rounding errors prevent the line search from converging'
else:
msg = "The line search algorithm could not find a solution " + \
"less than or equal to amax: %s" % amax
warn(msg, LineSearchWarning)
break
if (phi_a1 > phi0 + c1 * alpha1 * derphi0) or \
((phi_a1 >= phi_a0) and (i > 1)):
alpha_star, phi_star, derphi_star = \
_zoom(alpha0, alpha1, phi_a0,
phi_a1, derphi_a0, phi, derphi,
phi0, derphi0, c1, c2, extra_condition)
break
derphi_a1 = derphi(alpha1)
if (abs(derphi_a1) <= -c2*derphi0):
if extra_condition(alpha1, phi_a1):
alpha_star = alpha1
phi_star = phi_a1
derphi_star = derphi_a1
break
if (derphi_a1 >= 0):
alpha_star, phi_star, derphi_star = \
_zoom(alpha1, alpha0, phi_a1,
phi_a0, derphi_a1, phi, derphi,
phi0, derphi0, c1, c2, extra_condition)
break
alpha2 = 2 * alpha1 # increase by factor of two on each iteration
if amax is not None:
alpha2 = min(alpha2, amax)
alpha0 = alpha1
alpha1 = alpha2
phi_a0 = phi_a1
phi_a1 = phi(alpha1)
derphi_a0 = derphi_a1
else:
# stopping test maxiter reached
alpha_star = alpha1
phi_star = phi_a1
derphi_star = None
warn('The line search algorithm did not converge', LineSearchWarning)
return alpha_star, phi_star, phi0, derphi_star
def _cubicmin(a, fa, fpa, b, fb, c, fc):
"""
Finds the minimizer for a cubic polynomial that goes through the
points (a,fa), (b,fb), and (c,fc) with derivative at a of fpa.
If no minimizer can be found return None
"""
# f(x) = A *(x-a)^3 + B*(x-a)^2 + C*(x-a) + D
with np.errstate(divide='raise', over='raise', invalid='raise'):
try:
C = fpa
db = b - a
dc = c - a
denom = (db * dc) ** 2 * (db - dc)
d1 = np.empty((2, 2))
d1[0, 0] = dc ** 2
d1[0, 1] = -db ** 2
d1[1, 0] = -dc ** 3
d1[1, 1] = db ** 3
[A, B] = np.dot(d1, np.asarray([fb - fa - C * db,
fc - fa - C * dc]).flatten())
A /= denom
B /= denom
radical = B * B - 3 * A * C
xmin = a + (-B + np.sqrt(radical)) / (3 * A)
except ArithmeticError:
return None
if not np.isfinite(xmin):
return None
return xmin
def _quadmin(a, fa, fpa, b, fb):
"""
Finds the minimizer for a quadratic polynomial that goes through
the points (a,fa), (b,fb) with derivative at a of fpa,
"""
# f(x) = B*(x-a)^2 + C*(x-a) + D
with np.errstate(divide='raise', over='raise', invalid='raise'):
try:
D = fa
C = fpa
db = b - a * 1.0
B = (fb - D - C * db) / (db * db)
xmin = a - C / (2.0 * B)
except ArithmeticError:
return None
if not np.isfinite(xmin):
return None
return xmin
def _zoom(a_lo, a_hi, phi_lo, phi_hi, derphi_lo,
phi, derphi, phi0, derphi0, c1, c2, extra_condition):
"""
Part of the optimization algorithm in `scalar_search_wolfe2`.
"""
maxiter = 10
i = 0
delta1 = 0.2 # cubic interpolant check
delta2 = 0.1 # quadratic interpolant check
phi_rec = phi0
a_rec = 0
while True:
# interpolate to find a trial step length between a_lo and
# a_hi Need to choose interpolation here. Use cubic
# interpolation and then if the result is within delta *
# dalpha or outside of the interval bounded by a_lo or a_hi
# then use quadratic interpolation, if the result is still too
# close, then use bisection
dalpha = a_hi - a_lo
if dalpha < 0:
a, b = a_hi, a_lo
else:
a, b = a_lo, a_hi
# minimizer of cubic interpolant
# (uses phi_lo, derphi_lo, phi_hi, and the most recent value of phi)
#
# if the result is too close to the end points (or out of the
# interval) then use quadratic interpolation with phi_lo,
# derphi_lo and phi_hi if the result is still too close to the
# end points (or out of the interval) then use bisection
if (i > 0):
cchk = delta1 * dalpha
a_j = _cubicmin(a_lo, phi_lo, derphi_lo, a_hi, phi_hi,
a_rec, phi_rec)
if (i == 0) or (a_j is None) or (a_j > b - cchk) or (a_j < a + cchk):
qchk = delta2 * dalpha
a_j = _quadmin(a_lo, phi_lo, derphi_lo, a_hi, phi_hi)
if (a_j is None) or (a_j > b-qchk) or (a_j < a+qchk):
a_j = a_lo + 0.5*dalpha
# Check new value of a_j
phi_aj = phi(a_j)
if (phi_aj > phi0 + c1*a_j*derphi0) or (phi_aj >= phi_lo):
phi_rec = phi_hi
a_rec = a_hi
a_hi = a_j
phi_hi = phi_aj
else:
derphi_aj = derphi(a_j)
if abs(derphi_aj) <= -c2*derphi0 and extra_condition(a_j, phi_aj):
a_star = a_j
val_star = phi_aj
valprime_star = derphi_aj
break
if derphi_aj*(a_hi - a_lo) >= 0:
phi_rec = phi_hi
a_rec = a_hi
a_hi = a_lo
phi_hi = phi_lo
else:
phi_rec = phi_lo
a_rec = a_lo
a_lo = a_j
phi_lo = phi_aj
derphi_lo = derphi_aj
i += 1
if (i > maxiter):
# Failed to find a conforming step size
a_star = None
val_star = None
valprime_star = None
break
return a_star, val_star, valprime_star
#------------------------------------------------------------------------------
# Armijo line and scalar searches
#------------------------------------------------------------------------------
def line_search_armijo(f, xk, pk, gfk, old_fval, args=(), c1=1e-4, alpha0=1):
"""Minimize over alpha, the function ``f(xk+alpha pk)``.
Parameters
----------
f : callable
Function to be minimized.
xk : array_like
Current point.
pk : array_like
Search direction.
gfk : array_like
Gradient of `f` at point `xk`.
old_fval : float
Value of `f` at point `xk`.
args : tuple, optional
Optional arguments.
c1 : float, optional
Value to control stopping criterion.
alpha0 : scalar, optional
Value of `alpha` at start of the optimization.
Returns
-------
alpha
f_count
f_val_at_alpha
Notes
-----
Uses the interpolation algorithm (Armijo backtracking) as suggested by
Wright and Nocedal in 'Numerical Optimization', 1999, pg. 56-57
"""
xk = np.atleast_1d(xk)
fc = [0]
def phi(alpha1):
fc[0] += 1
return f(xk + alpha1*pk, *args)
if old_fval is None:
phi0 = phi(0.)
else:
phi0 = old_fval # compute f(xk) -- done in past loop
derphi0 = np.dot(gfk, pk)
alpha, phi1 = scalar_search_armijo(phi, phi0, derphi0, c1=c1,
alpha0=alpha0)
return alpha, fc[0], phi1
def line_search_BFGS(f, xk, pk, gfk, old_fval, args=(), c1=1e-4, alpha0=1):
"""
Compatibility wrapper for `line_search_armijo`
"""
r = line_search_armijo(f, xk, pk, gfk, old_fval, args=args, c1=c1,
alpha0=alpha0)
return r[0], r[1], 0, r[2]
def scalar_search_armijo(phi, phi0, derphi0, c1=1e-4, alpha0=1, amin=0):
"""Minimize over alpha, the function ``phi(alpha)``.
Uses the interpolation algorithm (Armijo backtracking) as suggested by
Wright and Nocedal in 'Numerical Optimization', 1999, pg. 56-57
alpha > 0 is assumed to be a descent direction.
Returns
-------
alpha
phi1
"""
phi_a0 = phi(alpha0)
if phi_a0 <= phi0 + c1*alpha0*derphi0:
return alpha0, phi_a0
# Otherwise compute the minimizer of a quadratic interpolant:
alpha1 = -(derphi0) * alpha0**2 / 2.0 / (phi_a0 - phi0 - derphi0 * alpha0)
phi_a1 = phi(alpha1)
if (phi_a1 <= phi0 + c1*alpha1*derphi0):
return alpha1, phi_a1
# Otherwise loop with cubic interpolation until we find an alpha which
# satisfies the first Wolfe condition (since we are backtracking, we will
# assume that the value of alpha is not too small and satisfies the second
# condition.
while alpha1 > amin: # we are assuming alpha>0 is a descent direction
factor = alpha0**2 * alpha1**2 * (alpha1-alpha0)
a = alpha0**2 * (phi_a1 - phi0 - derphi0*alpha1) - \
alpha1**2 * (phi_a0 - phi0 - derphi0*alpha0)
a = a / factor
b = -alpha0**3 * (phi_a1 - phi0 - derphi0*alpha1) + \
alpha1**3 * (phi_a0 - phi0 - derphi0*alpha0)
b = b / factor
alpha2 = (-b + np.sqrt(abs(b**2 - 3 * a * derphi0))) / (3.0*a)
phi_a2 = phi(alpha2)
if (phi_a2 <= phi0 + c1*alpha2*derphi0):
return alpha2, phi_a2
if (alpha1 - alpha2) > alpha1 / 2.0 or (1 - alpha2/alpha1) < 0.96:
alpha2 = alpha1 / 2.0
alpha0 = alpha1
alpha1 = alpha2
phi_a0 = phi_a1
phi_a1 = phi_a2
# Failed to find a suitable step length
return None, phi_a1
#------------------------------------------------------------------------------
# Non-monotone line search for DF-SANE
#------------------------------------------------------------------------------
def _nonmonotone_line_search_cruz(f, x_k, d, prev_fs, eta,
gamma=1e-4, tau_min=0.1, tau_max=0.5):
"""
Nonmonotone backtracking line search as described in [1]_
Parameters
----------
f : callable
Function returning a tuple ``(f, F)`` where ``f`` is the value
of a merit function and ``F`` the residual.
x_k : ndarray
Initial position
d : ndarray
Search direction
prev_fs : float
List of previous merit function values. Should have ``len(prev_fs) <= M``
where ``M`` is the nonmonotonicity window parameter.
eta : float
Allowed merit function increase, see [1]_
gamma, tau_min, tau_max : float, optional
Search parameters, see [1]_
Returns
-------
alpha : float
Step length
xp : ndarray
Next position
fp : float
Merit function value at next position
Fp : ndarray
Residual at next position
References
----------
[1] "Spectral residual method without gradient information for solving
large-scale nonlinear systems of equations." W. La Cruz,
J.M. Martinez, M. Raydan. Math. Comp. **75**, 1429 (2006).
"""
f_k = prev_fs[-1]
f_bar = max(prev_fs)
alpha_p = 1
alpha_m = 1
alpha = 1
while True:
xp = x_k + alpha_p * d
fp, Fp = f(xp)
if fp <= f_bar + eta - gamma * alpha_p**2 * f_k:
alpha = alpha_p
break
alpha_tp = alpha_p**2 * f_k / (fp + (2*alpha_p - 1)*f_k)
xp = x_k - alpha_m * d
fp, Fp = f(xp)
if fp <= f_bar + eta - gamma * alpha_m**2 * f_k:
alpha = -alpha_m
break
alpha_tm = alpha_m**2 * f_k / (fp + (2*alpha_m - 1)*f_k)
alpha_p = np.clip(alpha_tp, tau_min * alpha_p, tau_max * alpha_p)
alpha_m = np.clip(alpha_tm, tau_min * alpha_m, tau_max * alpha_m)
return alpha, xp, fp, Fp
def _nonmonotone_line_search_cheng(f, x_k, d, f_k, C, Q, eta,
gamma=1e-4, tau_min=0.1, tau_max=0.5,
nu=0.85):
"""
Nonmonotone line search from [1]
Parameters
----------
f : callable
Function returning a tuple ``(f, F)`` where ``f`` is the value
of a merit function and ``F`` the residual.
x_k : ndarray
Initial position
d : ndarray
Search direction
f_k : float
Initial merit function value
C, Q : float
Control parameters. On the first iteration, give values
Q=1.0, C=f_k
eta : float
Allowed merit function increase, see [1]_
nu, gamma, tau_min, tau_max : float, optional
Search parameters, see [1]_
Returns
-------
alpha : float
Step length
xp : ndarray
Next position
fp : float
Merit function value at next position
Fp : ndarray
Residual at next position
C : float
New value for the control parameter C
Q : float
New value for the control parameter Q
References
----------
.. [1] W. Cheng & D.-H. Li, ''A derivative-free nonmonotone line
search and its application to the spectral residual
method'', IMA J. Numer. Anal. 29, 814 (2009).
"""
alpha_p = 1
alpha_m = 1
alpha = 1
while True:
xp = x_k + alpha_p * d
fp, Fp = f(xp)
if fp <= C + eta - gamma * alpha_p**2 * f_k:
alpha = alpha_p
break
alpha_tp = alpha_p**2 * f_k / (fp + (2*alpha_p - 1)*f_k)
xp = x_k - alpha_m * d
fp, Fp = f(xp)
if fp <= C + eta - gamma * alpha_m**2 * f_k:
alpha = -alpha_m
break
alpha_tm = alpha_m**2 * f_k / (fp + (2*alpha_m - 1)*f_k)
alpha_p = np.clip(alpha_tp, tau_min * alpha_p, tau_max * alpha_p)
alpha_m = np.clip(alpha_tm, tau_min * alpha_m, tau_max * alpha_m)
# Update C and Q
Q_next = nu * Q + 1
C = (nu * Q * (C + eta) + fp) / Q_next
Q = Q_next
return alpha, xp, fp, Fp, C, Q
| 26,489 | 29.102273 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_basinhopping.py
|
"""
basinhopping: The basinhopping global optimization algorithm
"""
from __future__ import division, print_function, absolute_import
import numpy as np
import math
from numpy import cos, sin
import scipy.optimize
import collections
from scipy._lib._util import check_random_state
__all__ = ['basinhopping']
class Storage(object):
"""
Class used to store the lowest energy structure
"""
def __init__(self, minres):
self._add(minres)
def _add(self, minres):
self.minres = minres
self.minres.x = np.copy(minres.x)
def update(self, minres):
if minres.fun < self.minres.fun:
self._add(minres)
return True
else:
return False
def get_lowest(self):
return self.minres
class BasinHoppingRunner(object):
"""This class implements the core of the basinhopping algorithm.
x0 : ndarray
The starting coordinates.
minimizer : callable
The local minimizer, with signature ``result = minimizer(x)``.
The return value is an `optimize.OptimizeResult` object.
step_taking : callable
This function displaces the coordinates randomly. Signature should
be ``x_new = step_taking(x)``. Note that `x` may be modified in-place.
accept_tests : list of callables
Each test is passed the kwargs `f_new`, `x_new`, `f_old` and
`x_old`. These tests will be used to judge whether or not to accept
the step. The acceptable return values are True, False, or ``"force
accept"``. If any of the tests return False then the step is rejected.
If ``"force accept"``, then this will override any other tests in
order to accept the step. This can be used, for example, to forcefully
escape from a local minimum that ``basinhopping`` is trapped in.
disp : bool, optional
Display status messages.
"""
def __init__(self, x0, minimizer, step_taking, accept_tests, disp=False):
self.x = np.copy(x0)
self.minimizer = minimizer
self.step_taking = step_taking
self.accept_tests = accept_tests
self.disp = disp
self.nstep = 0
# initialize return object
self.res = scipy.optimize.OptimizeResult()
self.res.minimization_failures = 0
# do initial minimization
minres = minimizer(self.x)
if not minres.success:
self.res.minimization_failures += 1
if self.disp:
print("warning: basinhopping: local minimization failure")
self.x = np.copy(minres.x)
self.energy = minres.fun
if self.disp:
print("basinhopping step %d: f %g" % (self.nstep, self.energy))
# initialize storage class
self.storage = Storage(minres)
if hasattr(minres, "nfev"):
self.res.nfev = minres.nfev
if hasattr(minres, "njev"):
self.res.njev = minres.njev
if hasattr(minres, "nhev"):
self.res.nhev = minres.nhev
def _monte_carlo_step(self):
"""Do one Monte Carlo iteration
Randomly displace the coordinates, minimize, and decide whether
or not to accept the new coordinates.
"""
# Take a random step. Make a copy of x because the step_taking
# algorithm might change x in place
x_after_step = np.copy(self.x)
x_after_step = self.step_taking(x_after_step)
# do a local minimization
minres = self.minimizer(x_after_step)
x_after_quench = minres.x
energy_after_quench = minres.fun
if not minres.success:
self.res.minimization_failures += 1
if self.disp:
print("warning: basinhopping: local minimization failure")
if hasattr(minres, "nfev"):
self.res.nfev += minres.nfev
if hasattr(minres, "njev"):
self.res.njev += minres.njev
if hasattr(minres, "nhev"):
self.res.nhev += minres.nhev
# accept the move based on self.accept_tests. If any test is False,
# then reject the step. If any test returns the special string
# 'force accept', then accept the step regardless. This can be used
# to forcefully escape from a local minimum if normal basin hopping
# steps are not sufficient.
accept = True
for test in self.accept_tests:
testres = test(f_new=energy_after_quench, x_new=x_after_quench,
f_old=self.energy, x_old=self.x)
if testres == 'force accept':
accept = True
break
elif testres is None:
raise ValueError("accept_tests must return True, False, or "
"'force accept'")
elif not testres:
accept = False
# Report the result of the acceptance test to the take step class.
# This is for adaptive step taking
if hasattr(self.step_taking, "report"):
self.step_taking.report(accept, f_new=energy_after_quench,
x_new=x_after_quench, f_old=self.energy,
x_old=self.x)
return accept, minres
def one_cycle(self):
"""Do one cycle of the basinhopping algorithm
"""
self.nstep += 1
new_global_min = False
accept, minres = self._monte_carlo_step()
if accept:
self.energy = minres.fun
self.x = np.copy(minres.x)
new_global_min = self.storage.update(minres)
# print some information
if self.disp:
self.print_report(minres.fun, accept)
if new_global_min:
print("found new global minimum on step %d with function"
" value %g" % (self.nstep, self.energy))
# save some variables as BasinHoppingRunner attributes
self.xtrial = minres.x
self.energy_trial = minres.fun
self.accept = accept
return new_global_min
def print_report(self, energy_trial, accept):
"""print a status update"""
minres = self.storage.get_lowest()
print("basinhopping step %d: f %g trial_f %g accepted %d "
" lowest_f %g" % (self.nstep, self.energy, energy_trial,
accept, minres.fun))
class AdaptiveStepsize(object):
"""
Class to implement adaptive stepsize.
This class wraps the step taking class and modifies the stepsize to
ensure the true acceptance rate is as close as possible to the target.
Parameters
----------
takestep : callable
The step taking routine. Must contain modifiable attribute
takestep.stepsize
accept_rate : float, optional
The target step acceptance rate
interval : int, optional
Interval for how often to update the stepsize
factor : float, optional
The step size is multiplied or divided by this factor upon each
update.
verbose : bool, optional
Print information about each update
"""
def __init__(self, takestep, accept_rate=0.5, interval=50, factor=0.9,
verbose=True):
self.takestep = takestep
self.target_accept_rate = accept_rate
self.interval = interval
self.factor = factor
self.verbose = verbose
self.nstep = 0
self.nstep_tot = 0
self.naccept = 0
def __call__(self, x):
return self.take_step(x)
def _adjust_step_size(self):
old_stepsize = self.takestep.stepsize
accept_rate = float(self.naccept) / self.nstep
if accept_rate > self.target_accept_rate:
# We're accepting too many steps. This generally means we're
# trapped in a basin. Take bigger steps
self.takestep.stepsize /= self.factor
else:
# We're not accepting enough steps. Take smaller steps
self.takestep.stepsize *= self.factor
if self.verbose:
print("adaptive stepsize: acceptance rate %f target %f new "
"stepsize %g old stepsize %g" % (accept_rate,
self.target_accept_rate, self.takestep.stepsize,
old_stepsize))
def take_step(self, x):
self.nstep += 1
self.nstep_tot += 1
if self.nstep % self.interval == 0:
self._adjust_step_size()
return self.takestep(x)
def report(self, accept, **kwargs):
"called by basinhopping to report the result of the step"
if accept:
self.naccept += 1
class RandomDisplacement(object):
"""
Add a random displacement of maximum size `stepsize` to each coordinate
Calling this updates `x` in-place.
Parameters
----------
stepsize : float, optional
Maximum stepsize in any dimension
random_state : None or `np.random.RandomState` instance, optional
The random number generator that generates the displacements
"""
def __init__(self, stepsize=0.5, random_state=None):
self.stepsize = stepsize
self.random_state = check_random_state(random_state)
def __call__(self, x):
x += self.random_state.uniform(-self.stepsize, self.stepsize,
np.shape(x))
return x
class MinimizerWrapper(object):
"""
wrap a minimizer function as a minimizer class
"""
def __init__(self, minimizer, func=None, **kwargs):
self.minimizer = minimizer
self.func = func
self.kwargs = kwargs
def __call__(self, x0):
if self.func is None:
return self.minimizer(x0, **self.kwargs)
else:
return self.minimizer(self.func, x0, **self.kwargs)
class Metropolis(object):
"""
Metropolis acceptance criterion
Parameters
----------
T : float
The "temperature" parameter for the accept or reject criterion.
random_state : None or `np.random.RandomState` object
Random number generator used for acceptance test
"""
def __init__(self, T, random_state=None):
# Avoid ZeroDivisionError since "MBH can be regarded as a special case
# of the BH framework with the Metropolis criterion, where temperature
# T = 0." (Reject all steps that increase energy.)
self.beta = 1.0 / T if T != 0 else float('inf')
self.random_state = check_random_state(random_state)
def accept_reject(self, energy_new, energy_old):
"""
If new energy is lower than old, it will always be accepted.
If new is higher than old, there is a chance it will be accepted,
less likely for larger differences.
"""
w = math.exp(min(0, -float(energy_new - energy_old) * self.beta))
rand = self.random_state.rand()
return w >= rand
def __call__(self, **kwargs):
"""
f_new and f_old are mandatory in kwargs
"""
return bool(self.accept_reject(kwargs["f_new"],
kwargs["f_old"]))
def basinhopping(func, x0, niter=100, T=1.0, stepsize=0.5,
minimizer_kwargs=None, take_step=None, accept_test=None,
callback=None, interval=50, disp=False, niter_success=None,
seed=None):
"""
Find the global minimum of a function using the basin-hopping algorithm
Basin-hopping is a two-phase method that combines a global stepping
algorithm with local minimization at each step. Designed to mimic
the natural process of energy minimization of clusters of atoms, it works
well for similar problems with "funnel-like, but rugged" energy landscapes
[5]_.
As the step-taking, step acceptance, and minimization methods are all
customizable, this function can also be used to implement other two-phase
methods.
Parameters
----------
func : callable ``f(x, *args)``
Function to be optimized. ``args`` can be passed as an optional item
in the dict ``minimizer_kwargs``
x0 : array_like
Initial guess.
niter : integer, optional
The number of basin-hopping iterations
T : float, optional
The "temperature" parameter for the accept or reject criterion. Higher
"temperatures" mean that larger jumps in function value will be
accepted. For best results ``T`` should be comparable to the
separation (in function value) between local minima.
stepsize : float, optional
Maximum step size for use in the random displacement.
minimizer_kwargs : dict, optional
Extra keyword arguments to be passed to the local minimizer
``scipy.optimize.minimize()`` Some important options could be:
method : str
The minimization method (e.g. ``"L-BFGS-B"``)
args : tuple
Extra arguments passed to the objective function (``func``) and
its derivatives (Jacobian, Hessian).
take_step : callable ``take_step(x)``, optional
Replace the default step-taking routine with this routine. The default
step-taking routine is a random displacement of the coordinates, but
other step-taking algorithms may be better for some systems.
``take_step`` can optionally have the attribute ``take_step.stepsize``.
If this attribute exists, then ``basinhopping`` will adjust
``take_step.stepsize`` in order to try to optimize the global minimum
search.
accept_test : callable, ``accept_test(f_new=f_new, x_new=x_new, f_old=fold, x_old=x_old)``, optional
Define a test which will be used to judge whether or not to accept the
step. This will be used in addition to the Metropolis test based on
"temperature" ``T``. The acceptable return values are True,
False, or ``"force accept"``. If any of the tests return False
then the step is rejected. If the latter, then this will override any
other tests in order to accept the step. This can be used, for example,
to forcefully escape from a local minimum that ``basinhopping`` is
trapped in.
callback : callable, ``callback(x, f, accept)``, optional
A callback function which will be called for all minima found. ``x``
and ``f`` are the coordinates and function value of the trial minimum,
and ``accept`` is whether or not that minimum was accepted. This can
be used, for example, to save the lowest N minima found. Also,
``callback`` can be used to specify a user defined stop criterion by
optionally returning True to stop the ``basinhopping`` routine.
interval : integer, optional
interval for how often to update the ``stepsize``
disp : bool, optional
Set to True to print status messages
niter_success : integer, optional
Stop the run if the global minimum candidate remains the same for this
number of iterations.
seed : int or `np.random.RandomState`, optional
If `seed` is not specified the `np.RandomState` singleton is used.
If `seed` is an int, a new `np.random.RandomState` instance is used,
seeded with seed.
If `seed` is already a `np.random.RandomState instance`, then that
`np.random.RandomState` instance is used.
Specify `seed` for repeatable minimizations. The random numbers
generated with this seed only affect the default Metropolis
`accept_test` and the default `take_step`. If you supply your own
`take_step` and `accept_test`, and these functions use random
number generation, then those functions are responsible for the state
of their random number generator.
Returns
-------
res : OptimizeResult
The optimization result represented as a ``OptimizeResult`` object.
Important attributes are: ``x`` the solution array, ``fun`` the value
of the function at the solution, and ``message`` which describes the
cause of the termination. The ``OptimizeResult`` object returned by the
selected minimizer at the lowest minimum is also contained within this
object and can be accessed through the ``lowest_optimization_result``
attribute. See `OptimizeResult` for a description of other attributes.
See Also
--------
minimize :
The local minimization function called once for each basinhopping step.
``minimizer_kwargs`` is passed to this routine.
Notes
-----
Basin-hopping is a stochastic algorithm which attempts to find the global
minimum of a smooth scalar function of one or more variables [1]_ [2]_ [3]_
[4]_. The algorithm in its current form was described by David Wales and
Jonathan Doye [2]_ http://www-wales.ch.cam.ac.uk/.
The algorithm is iterative with each cycle composed of the following
features
1) random perturbation of the coordinates
2) local minimization
3) accept or reject the new coordinates based on the minimized function
value
The acceptance test used here is the Metropolis criterion of standard Monte
Carlo algorithms, although there are many other possibilities [3]_.
This global minimization method has been shown to be extremely efficient
for a wide variety of problems in physics and chemistry. It is
particularly useful when the function has many minima separated by large
barriers. See the Cambridge Cluster Database
http://www-wales.ch.cam.ac.uk/CCD.html for databases of molecular systems
that have been optimized primarily using basin-hopping. This database
includes minimization problems exceeding 300 degrees of freedom.
See the free software program GMIN (http://www-wales.ch.cam.ac.uk/GMIN) for
a Fortran implementation of basin-hopping. This implementation has many
different variations of the procedure described above, including more
advanced step taking algorithms and alternate acceptance criterion.
For stochastic global optimization there is no way to determine if the true
global minimum has actually been found. Instead, as a consistency check,
the algorithm can be run from a number of different random starting points
to ensure the lowest minimum found in each example has converged to the
global minimum. For this reason ``basinhopping`` will by default simply
run for the number of iterations ``niter`` and return the lowest minimum
found. It is left to the user to ensure that this is in fact the global
minimum.
Choosing ``stepsize``: This is a crucial parameter in ``basinhopping`` and
depends on the problem being solved. The step is chosen uniformly in the
region from x0-stepsize to x0+stepsize, in each dimension. Ideally it
should be comparable to the typical separation (in argument values) between
local minima of the function being optimized. ``basinhopping`` will, by
default, adjust ``stepsize`` to find an optimal value, but this may take
many iterations. You will get quicker results if you set a sensible
initial value for ``stepsize``.
Choosing ``T``: The parameter ``T`` is the "temperature" used in the
Metropolis criterion. Basinhopping steps are always accepted if
``func(xnew) < func(xold)``. Otherwise, they are accepted with
probability::
exp( -(func(xnew) - func(xold)) / T )
So, for best results, ``T`` should to be comparable to the typical
difference (in function values) between local minima. (The height of
"walls" between local minima is irrelevant.)
If ``T`` is 0, the algorithm becomes Monotonic Basin-Hopping, in which all
steps that increase energy are rejected.
.. versionadded:: 0.12.0
References
----------
.. [1] Wales, David J. 2003, Energy Landscapes, Cambridge University Press,
Cambridge, UK.
.. [2] Wales, D J, and Doye J P K, Global Optimization by Basin-Hopping and
the Lowest Energy Structures of Lennard-Jones Clusters Containing up to
110 Atoms. Journal of Physical Chemistry A, 1997, 101, 5111.
.. [3] Li, Z. and Scheraga, H. A., Monte Carlo-minimization approach to the
multiple-minima problem in protein folding, Proc. Natl. Acad. Sci. USA,
1987, 84, 6611.
.. [4] Wales, D. J. and Scheraga, H. A., Global optimization of clusters,
crystals, and biomolecules, Science, 1999, 285, 1368.
.. [5] Olson, B., Hashmi, I., Molloy, K., and Shehu1, A., Basin Hopping as
a General and Versatile Optimization Framework for the Characterization
of Biological Macromolecules, Advances in Artificial Intelligence,
Volume 2012 (2012), Article ID 674832, :doi:`10.1155/2012/674832`
Examples
--------
The following example is a one-dimensional minimization problem, with many
local minima superimposed on a parabola.
>>> from scipy.optimize import basinhopping
>>> func = lambda x: np.cos(14.5 * x - 0.3) + (x + 0.2) * x
>>> x0=[1.]
Basinhopping, internally, uses a local minimization algorithm. We will use
the parameter ``minimizer_kwargs`` to tell basinhopping which algorithm to
use and how to set up that minimizer. This parameter will be passed to
``scipy.optimize.minimize()``.
>>> minimizer_kwargs = {"method": "BFGS"}
>>> ret = basinhopping(func, x0, minimizer_kwargs=minimizer_kwargs,
... niter=200)
>>> print("global minimum: x = %.4f, f(x0) = %.4f" % (ret.x, ret.fun))
global minimum: x = -0.1951, f(x0) = -1.0009
Next consider a two-dimensional minimization problem. Also, this time we
will use gradient information to significantly speed up the search.
>>> def func2d(x):
... f = np.cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] +
... 0.2) * x[0]
... df = np.zeros(2)
... df[0] = -14.5 * np.sin(14.5 * x[0] - 0.3) + 2. * x[0] + 0.2
... df[1] = 2. * x[1] + 0.2
... return f, df
We'll also use a different local minimization algorithm. Also we must tell
the minimizer that our function returns both energy and gradient (jacobian)
>>> minimizer_kwargs = {"method":"L-BFGS-B", "jac":True}
>>> x0 = [1.0, 1.0]
>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
... niter=200)
>>> print("global minimum: x = [%.4f, %.4f], f(x0) = %.4f" % (ret.x[0],
... ret.x[1],
... ret.fun))
global minimum: x = [-0.1951, -0.1000], f(x0) = -1.0109
Here is an example using a custom step-taking routine. Imagine you want
the first coordinate to take larger steps than the rest of the coordinates.
This can be implemented like so:
>>> class MyTakeStep(object):
... def __init__(self, stepsize=0.5):
... self.stepsize = stepsize
... def __call__(self, x):
... s = self.stepsize
... x[0] += np.random.uniform(-2.*s, 2.*s)
... x[1:] += np.random.uniform(-s, s, x[1:].shape)
... return x
Since ``MyTakeStep.stepsize`` exists basinhopping will adjust the magnitude
of ``stepsize`` to optimize the search. We'll use the same 2-D function as
before
>>> mytakestep = MyTakeStep()
>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
... niter=200, take_step=mytakestep)
>>> print("global minimum: x = [%.4f, %.4f], f(x0) = %.4f" % (ret.x[0],
... ret.x[1],
... ret.fun))
global minimum: x = [-0.1951, -0.1000], f(x0) = -1.0109
Now let's do an example using a custom callback function which prints the
value of every minimum found
>>> def print_fun(x, f, accepted):
... print("at minimum %.4f accepted %d" % (f, int(accepted)))
We'll run it for only 10 basinhopping steps this time.
>>> np.random.seed(1)
>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
... niter=10, callback=print_fun)
at minimum 0.4159 accepted 1
at minimum -0.9073 accepted 1
at minimum -0.1021 accepted 1
at minimum -0.1021 accepted 1
at minimum 0.9102 accepted 1
at minimum 0.9102 accepted 1
at minimum 2.2945 accepted 0
at minimum -0.1021 accepted 1
at minimum -1.0109 accepted 1
at minimum -1.0109 accepted 1
The minimum at -1.0109 is actually the global minimum, found already on the
8th iteration.
Now let's implement bounds on the problem using a custom ``accept_test``:
>>> class MyBounds(object):
... def __init__(self, xmax=[1.1,1.1], xmin=[-1.1,-1.1] ):
... self.xmax = np.array(xmax)
... self.xmin = np.array(xmin)
... def __call__(self, **kwargs):
... x = kwargs["x_new"]
... tmax = bool(np.all(x <= self.xmax))
... tmin = bool(np.all(x >= self.xmin))
... return tmax and tmin
>>> mybounds = MyBounds()
>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
... niter=10, accept_test=mybounds)
"""
x0 = np.array(x0)
# set up the np.random.RandomState generator
rng = check_random_state(seed)
# set up minimizer
if minimizer_kwargs is None:
minimizer_kwargs = dict()
wrapped_minimizer = MinimizerWrapper(scipy.optimize.minimize, func,
**minimizer_kwargs)
# set up step-taking algorithm
if take_step is not None:
if not isinstance(take_step, collections.Callable):
raise TypeError("take_step must be callable")
# if take_step.stepsize exists then use AdaptiveStepsize to control
# take_step.stepsize
if hasattr(take_step, "stepsize"):
take_step_wrapped = AdaptiveStepsize(take_step, interval=interval,
verbose=disp)
else:
take_step_wrapped = take_step
else:
# use default
displace = RandomDisplacement(stepsize=stepsize, random_state=rng)
take_step_wrapped = AdaptiveStepsize(displace, interval=interval,
verbose=disp)
# set up accept tests
if accept_test is not None:
if not isinstance(accept_test, collections.Callable):
raise TypeError("accept_test must be callable")
accept_tests = [accept_test]
else:
accept_tests = []
# use default
metropolis = Metropolis(T, random_state=rng)
accept_tests.append(metropolis)
if niter_success is None:
niter_success = niter + 2
bh = BasinHoppingRunner(x0, wrapped_minimizer, take_step_wrapped,
accept_tests, disp=disp)
# start main iteration loop
count, i = 0, 0
message = ["requested number of basinhopping iterations completed"
" successfully"]
for i in range(niter):
new_global_min = bh.one_cycle()
if isinstance(callback, collections.Callable):
# should we pass a copy of x?
val = callback(bh.xtrial, bh.energy_trial, bh.accept)
if val is not None:
if val:
message = ["callback function requested stop early by"
"returning True"]
break
count += 1
if new_global_min:
count = 0
elif count > niter_success:
message = ["success condition satisfied"]
break
# prepare return object
res = bh.res
res.lowest_optimization_result = bh.storage.get_lowest()
res.x = np.copy(res.lowest_optimization_result.x)
res.fun = res.lowest_optimization_result.fun
res.message = message
res.nit = i + 1
return res
def _test_func2d_nograd(x):
f = (cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] + 0.2) * x[0]
+ 1.010876184442655)
return f
def _test_func2d(x):
f = (cos(14.5 * x[0] - 0.3) + (x[0] + 0.2) * x[0] + cos(14.5 * x[1] -
0.3) + (x[1] + 0.2) * x[1] + x[0] * x[1] + 1.963879482144252)
df = np.zeros(2)
df[0] = -14.5 * sin(14.5 * x[0] - 0.3) + 2. * x[0] + 0.2 + x[1]
df[1] = -14.5 * sin(14.5 * x[1] - 0.3) + 2. * x[1] + 0.2 + x[0]
return f, df
if __name__ == "__main__":
print("\n\nminimize a 2d function without gradient")
# minimum expected at ~[-0.195, -0.1]
kwargs = {"method": "L-BFGS-B"}
x0 = np.array([1.0, 1.])
scipy.optimize.minimize(_test_func2d_nograd, x0, **kwargs)
ret = basinhopping(_test_func2d_nograd, x0, minimizer_kwargs=kwargs,
niter=200, disp=False)
print("minimum expected at func([-0.195, -0.1]) = 0.0")
print(ret)
print("\n\ntry a harder 2d problem")
kwargs = {"method": "L-BFGS-B", "jac": True}
x0 = np.array([1.0, 1.0])
ret = basinhopping(_test_func2d, x0, minimizer_kwargs=kwargs, niter=200,
disp=False)
print("minimum expected at ~, func([-0.19415263, -0.19415263]) = 0")
print(ret)
| 29,477 | 38.943089 | 104 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_trustregion_krylov.py
|
from ._trustregion import (_minimize_trust_region)
from ._trlib import (get_trlib_quadratic_subproblem)
__all__ = ['_minimize_trust_krylov']
def _minimize_trust_krylov(fun, x0, args=(), jac=None, hess=None, hessp=None,
inexact=True, **trust_region_options):
"""
Minimization of a scalar function of one or more variables using
a nearly exact trust-region algorithm that only requires matrix
vector products with the hessian matrix.
Options
-------
inexact : bool, optional
Accuracy to solve subproblems. If True requires less nonlinear
iterations, but more vector products.
.. versionadded:: 1.0.0
"""
if jac is None:
raise ValueError('Jacobian is required for trust region ',
'exact minimization.')
if hess is None and hessp is None:
raise ValueError('Either the Hessian or the Hessian-vector product '
'is required for Krylov trust-region minimization')
# tol_rel specifies the termination tolerance relative to the initial
# gradient norm in the krylov subspace iteration.
# - tol_rel_i specifies the tolerance for interior convergence.
# - tol_rel_b specifies the tolerance for boundary convergence.
# in nonlinear programming applications it is not necessary to solve
# the boundary case as exact as the interior case.
# - setting tol_rel_i=-2 leads to a forcing sequence in the krylov
# subspace iteration leading to quadratic convergence if eventually
# the trust region stays inactive.
# - setting tol_rel_b=-3 leads to a forcing sequence in the krylov
# subspace iteration leading to superlinear convergence as long
# as the iterates hit the trust region boundary.
# For details consult the documentation of trlib_krylov_min
# in _trlib/trlib_krylov.h
#
# Optimality of this choice of parameters among a range of possibilities
# has been tested on the unconstrained subset of the CUTEst library.
if inexact:
return _minimize_trust_region(fun, x0, args=args, jac=jac,
hess=hess, hessp=hessp,
subproblem=get_trlib_quadratic_subproblem(
tol_rel_i=-2.0, tol_rel_b=-3.0,
disp=trust_region_options.get('disp', False)
),
**trust_region_options)
else:
return _minimize_trust_region(fun, x0, args=args, jac=jac,
hess=hess, hessp=hessp,
subproblem=get_trlib_quadratic_subproblem(
tol_rel_i=1e-8, tol_rel_b=1e-6,
disp=trust_region_options.get('disp', False)
),
**trust_region_options)
| 3,030 | 44.924242 | 86 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/slsqp.py
|
"""
This module implements the Sequential Least SQuares Programming optimization
algorithm (SLSQP), originally developed by Dieter Kraft.
See http://www.netlib.org/toms/733
Functions
---------
.. autosummary::
:toctree: generated/
approx_jacobian
fmin_slsqp
"""
from __future__ import division, print_function, absolute_import
__all__ = ['approx_jacobian', 'fmin_slsqp']
import numpy as np
from scipy.optimize._slsqp import slsqp
from numpy import (zeros, array, linalg, append, asfarray, concatenate, finfo,
sqrt, vstack, exp, inf, isfinite, atleast_1d)
from .optimize import wrap_function, OptimizeResult, _check_unknown_options
__docformat__ = "restructuredtext en"
_epsilon = sqrt(finfo(float).eps)
def approx_jacobian(x, func, epsilon, *args):
"""
Approximate the Jacobian matrix of a callable function.
Parameters
----------
x : array_like
The state vector at which to compute the Jacobian matrix.
func : callable f(x,*args)
The vector-valued function.
epsilon : float
The perturbation used to determine the partial derivatives.
args : sequence
Additional arguments passed to func.
Returns
-------
An array of dimensions ``(lenf, lenx)`` where ``lenf`` is the length
of the outputs of `func`, and ``lenx`` is the number of elements in
`x`.
Notes
-----
The approximation is done using forward differences.
"""
x0 = asfarray(x)
f0 = atleast_1d(func(*((x0,)+args)))
jac = zeros([len(x0), len(f0)])
dx = zeros(len(x0))
for i in range(len(x0)):
dx[i] = epsilon
jac[i] = (func(*((x0+dx,)+args)) - f0)/epsilon
dx[i] = 0.0
return jac.transpose()
def fmin_slsqp(func, x0, eqcons=(), f_eqcons=None, ieqcons=(), f_ieqcons=None,
bounds=(), fprime=None, fprime_eqcons=None,
fprime_ieqcons=None, args=(), iter=100, acc=1.0E-6,
iprint=1, disp=None, full_output=0, epsilon=_epsilon,
callback=None):
"""
Minimize a function using Sequential Least SQuares Programming
Python interface function for the SLSQP Optimization subroutine
originally implemented by Dieter Kraft.
Parameters
----------
func : callable f(x,*args)
Objective function. Must return a scalar.
x0 : 1-D ndarray of float
Initial guess for the independent variable(s).
eqcons : list, optional
A list of functions of length n such that
eqcons[j](x,*args) == 0.0 in a successfully optimized
problem.
f_eqcons : callable f(x,*args), optional
Returns a 1-D array in which each element must equal 0.0 in a
successfully optimized problem. If f_eqcons is specified,
eqcons is ignored.
ieqcons : list, optional
A list of functions of length n such that
ieqcons[j](x,*args) >= 0.0 in a successfully optimized
problem.
f_ieqcons : callable f(x,*args), optional
Returns a 1-D ndarray in which each element must be greater or
equal to 0.0 in a successfully optimized problem. If
f_ieqcons is specified, ieqcons is ignored.
bounds : list, optional
A list of tuples specifying the lower and upper bound
for each independent variable [(xl0, xu0),(xl1, xu1),...]
Infinite values will be interpreted as large floating values.
fprime : callable `f(x,*args)`, optional
A function that evaluates the partial derivatives of func.
fprime_eqcons : callable `f(x,*args)`, optional
A function of the form `f(x, *args)` that returns the m by n
array of equality constraint normals. If not provided,
the normals will be approximated. The array returned by
fprime_eqcons should be sized as ( len(eqcons), len(x0) ).
fprime_ieqcons : callable `f(x,*args)`, optional
A function of the form `f(x, *args)` that returns the m by n
array of inequality constraint normals. If not provided,
the normals will be approximated. The array returned by
fprime_ieqcons should be sized as ( len(ieqcons), len(x0) ).
args : sequence, optional
Additional arguments passed to func and fprime.
iter : int, optional
The maximum number of iterations.
acc : float, optional
Requested accuracy.
iprint : int, optional
The verbosity of fmin_slsqp :
* iprint <= 0 : Silent operation
* iprint == 1 : Print summary upon completion (default)
* iprint >= 2 : Print status of each iterate and summary
disp : int, optional
Over-rides the iprint interface (preferred).
full_output : bool, optional
If False, return only the minimizer of func (default).
Otherwise, output final objective function and summary
information.
epsilon : float, optional
The step size for finite-difference derivative estimates.
callback : callable, optional
Called after each iteration, as ``callback(x)``, where ``x`` is the
current parameter vector.
Returns
-------
out : ndarray of float
The final minimizer of func.
fx : ndarray of float, if full_output is true
The final value of the objective function.
its : int, if full_output is true
The number of iterations.
imode : int, if full_output is true
The exit mode from the optimizer (see below).
smode : string, if full_output is true
Message describing the exit mode from the optimizer.
See also
--------
minimize: Interface to minimization algorithms for multivariate
functions. See the 'SLSQP' `method` in particular.
Notes
-----
Exit modes are defined as follows ::
-1 : Gradient evaluation required (g & a)
0 : Optimization terminated successfully.
1 : Function evaluation required (f & c)
2 : More equality constraints than independent variables
3 : More than 3*n iterations in LSQ subproblem
4 : Inequality constraints incompatible
5 : Singular matrix E in LSQ subproblem
6 : Singular matrix C in LSQ subproblem
7 : Rank-deficient equality constraint subproblem HFTI
8 : Positive directional derivative for linesearch
9 : Iteration limit exceeded
Examples
--------
Examples are given :ref:`in the tutorial <tutorial-sqlsp>`.
"""
if disp is not None:
iprint = disp
opts = {'maxiter': iter,
'ftol': acc,
'iprint': iprint,
'disp': iprint != 0,
'eps': epsilon,
'callback': callback}
# Build the constraints as a tuple of dictionaries
cons = ()
# 1. constraints of the 1st kind (eqcons, ieqcons); no Jacobian; take
# the same extra arguments as the objective function.
cons += tuple({'type': 'eq', 'fun': c, 'args': args} for c in eqcons)
cons += tuple({'type': 'ineq', 'fun': c, 'args': args} for c in ieqcons)
# 2. constraints of the 2nd kind (f_eqcons, f_ieqcons) and their Jacobian
# (fprime_eqcons, fprime_ieqcons); also take the same extra arguments
# as the objective function.
if f_eqcons:
cons += ({'type': 'eq', 'fun': f_eqcons, 'jac': fprime_eqcons,
'args': args}, )
if f_ieqcons:
cons += ({'type': 'ineq', 'fun': f_ieqcons, 'jac': fprime_ieqcons,
'args': args}, )
res = _minimize_slsqp(func, x0, args, jac=fprime, bounds=bounds,
constraints=cons, **opts)
if full_output:
return res['x'], res['fun'], res['nit'], res['status'], res['message']
else:
return res['x']
def _minimize_slsqp(func, x0, args=(), jac=None, bounds=None,
constraints=(),
maxiter=100, ftol=1.0E-6, iprint=1, disp=False,
eps=_epsilon, callback=None,
**unknown_options):
"""
Minimize a scalar function of one or more variables using Sequential
Least SQuares Programming (SLSQP).
Options
-------
ftol : float
Precision goal for the value of f in the stopping criterion.
eps : float
Step size used for numerical approximation of the Jacobian.
disp : bool
Set to True to print convergence messages. If False,
`verbosity` is ignored and set to 0.
maxiter : int
Maximum number of iterations.
"""
_check_unknown_options(unknown_options)
fprime = jac
iter = maxiter
acc = ftol
epsilon = eps
if not disp:
iprint = 0
# Constraints are triaged per type into a dictionary of tuples
if isinstance(constraints, dict):
constraints = (constraints, )
cons = {'eq': (), 'ineq': ()}
for ic, con in enumerate(constraints):
# check type
try:
ctype = con['type'].lower()
except KeyError:
raise KeyError('Constraint %d has no type defined.' % ic)
except TypeError:
raise TypeError('Constraints must be defined using a '
'dictionary.')
except AttributeError:
raise TypeError("Constraint's type must be a string.")
else:
if ctype not in ['eq', 'ineq']:
raise ValueError("Unknown constraint type '%s'." % con['type'])
# check function
if 'fun' not in con:
raise ValueError('Constraint %d has no function defined.' % ic)
# check Jacobian
cjac = con.get('jac')
if cjac is None:
# approximate Jacobian function. The factory function is needed
# to keep a reference to `fun`, see gh-4240.
def cjac_factory(fun):
def cjac(x, *args):
return approx_jacobian(x, fun, epsilon, *args)
return cjac
cjac = cjac_factory(con['fun'])
# update constraints' dictionary
cons[ctype] += ({'fun': con['fun'],
'jac': cjac,
'args': con.get('args', ())}, )
exit_modes = {-1: "Gradient evaluation required (g & a)",
0: "Optimization terminated successfully.",
1: "Function evaluation required (f & c)",
2: "More equality constraints than independent variables",
3: "More than 3*n iterations in LSQ subproblem",
4: "Inequality constraints incompatible",
5: "Singular matrix E in LSQ subproblem",
6: "Singular matrix C in LSQ subproblem",
7: "Rank-deficient equality constraint subproblem HFTI",
8: "Positive directional derivative for linesearch",
9: "Iteration limit exceeded"}
# Wrap func
feval, func = wrap_function(func, args)
# Wrap fprime, if provided, or approx_jacobian if not
if fprime:
geval, fprime = wrap_function(fprime, args)
else:
geval, fprime = wrap_function(approx_jacobian, (func, epsilon))
# Transform x0 into an array.
x = asfarray(x0).flatten()
# Set the parameters that SLSQP will need
# meq, mieq: number of equality and inequality constraints
meq = sum(map(len, [atleast_1d(c['fun'](x, *c['args']))
for c in cons['eq']]))
mieq = sum(map(len, [atleast_1d(c['fun'](x, *c['args']))
for c in cons['ineq']]))
# m = The total number of constraints
m = meq + mieq
# la = The number of constraints, or 1 if there are no constraints
la = array([1, m]).max()
# n = The number of independent variables
n = len(x)
# Define the workspaces for SLSQP
n1 = n + 1
mineq = m - meq + n1 + n1
len_w = (3*n1+m)*(n1+1)+(n1-meq+1)*(mineq+2) + 2*mineq+(n1+mineq)*(n1-meq) \
+ 2*meq + n1 + ((n+1)*n)//2 + 2*m + 3*n + 3*n1 + 1
len_jw = mineq
w = zeros(len_w)
jw = zeros(len_jw)
# Decompose bounds into xl and xu
if bounds is None or len(bounds) == 0:
xl = np.empty(n, dtype=float)
xu = np.empty(n, dtype=float)
xl.fill(np.nan)
xu.fill(np.nan)
else:
bnds = array(bounds, float)
if bnds.shape[0] != n:
raise IndexError('SLSQP Error: the length of bounds is not '
'compatible with that of x0.')
with np.errstate(invalid='ignore'):
bnderr = bnds[:, 0] > bnds[:, 1]
if bnderr.any():
raise ValueError('SLSQP Error: lb > ub in bounds %s.' %
', '.join(str(b) for b in bnderr))
xl, xu = bnds[:, 0], bnds[:, 1]
# Mark infinite bounds with nans; the Fortran code understands this
infbnd = ~isfinite(bnds)
xl[infbnd[:, 0]] = np.nan
xu[infbnd[:, 1]] = np.nan
# Clip initial guess to bounds (SLSQP may fail with bounds-infeasible
# initial point)
have_bound = np.isfinite(xl)
x[have_bound] = np.clip(x[have_bound], xl[have_bound], np.inf)
have_bound = np.isfinite(xu)
x[have_bound] = np.clip(x[have_bound], -np.inf, xu[have_bound])
# Initialize the iteration counter and the mode value
mode = array(0, int)
acc = array(acc, float)
majiter = array(iter, int)
majiter_prev = 0
# Print the header if iprint >= 2
if iprint >= 2:
print("%5s %5s %16s %16s" % ("NIT", "FC", "OBJFUN", "GNORM"))
while 1:
if mode == 0 or mode == 1: # objective and constraint evaluation required
# Compute objective function
fx = func(x)
try:
fx = float(np.asarray(fx))
except (TypeError, ValueError):
raise ValueError("Objective function must return a scalar")
# Compute the constraints
if cons['eq']:
c_eq = concatenate([atleast_1d(con['fun'](x, *con['args']))
for con in cons['eq']])
else:
c_eq = zeros(0)
if cons['ineq']:
c_ieq = concatenate([atleast_1d(con['fun'](x, *con['args']))
for con in cons['ineq']])
else:
c_ieq = zeros(0)
# Now combine c_eq and c_ieq into a single matrix
c = concatenate((c_eq, c_ieq))
if mode == 0 or mode == -1: # gradient evaluation required
# Compute the derivatives of the objective function
# For some reason SLSQP wants g dimensioned to n+1
g = append(fprime(x), 0.0)
# Compute the normals of the constraints
if cons['eq']:
a_eq = vstack([con['jac'](x, *con['args'])
for con in cons['eq']])
else: # no equality constraint
a_eq = zeros((meq, n))
if cons['ineq']:
a_ieq = vstack([con['jac'](x, *con['args'])
for con in cons['ineq']])
else: # no inequality constraint
a_ieq = zeros((mieq, n))
# Now combine a_eq and a_ieq into a single a matrix
if m == 0: # no constraints
a = zeros((la, n))
else:
a = vstack((a_eq, a_ieq))
a = concatenate((a, zeros([la, 1])), 1)
# Call SLSQP
slsqp(m, meq, x, xl, xu, fx, c, g, a, acc, majiter, mode, w, jw)
# call callback if major iteration has incremented
if callback is not None and majiter > majiter_prev:
callback(np.copy(x))
# Print the status of the current iterate if iprint > 2 and the
# major iteration has incremented
if iprint >= 2 and majiter > majiter_prev:
print("%5i %5i % 16.6E % 16.6E" % (majiter, feval[0],
fx, linalg.norm(g)))
# If exit mode is not -1 or 1, slsqp has completed
if abs(mode) != 1:
break
majiter_prev = int(majiter)
# Optimization loop complete. Print status if requested
if iprint >= 1:
print(exit_modes[int(mode)] + " (Exit mode " + str(mode) + ')')
print(" Current function value:", fx)
print(" Iterations:", majiter)
print(" Function evaluations:", feval[0])
print(" Gradient evaluations:", geval[0])
return OptimizeResult(x=x, fun=fx, jac=g[:-1], nit=int(majiter),
nfev=feval[0], njev=geval[0], status=int(mode),
message=exit_modes[int(mode)], success=(mode == 0))
if __name__ == '__main__':
# objective function
def fun(x, r=[4, 2, 4, 2, 1]):
""" Objective function """
return exp(x[0]) * (r[0] * x[0]**2 + r[1] * x[1]**2 +
r[2] * x[0] * x[1] + r[3] * x[1] +
r[4])
# bounds
bnds = array([[-inf]*2, [inf]*2]).T
bnds[:, 0] = [0.1, 0.2]
# constraints
def feqcon(x, b=1):
""" Equality constraint """
return array([x[0]**2 + x[1] - b])
def jeqcon(x, b=1):
""" Jacobian of equality constraint """
return array([[2*x[0], 1]])
def fieqcon(x, c=10):
""" Inequality constraint """
return array([x[0] * x[1] + c])
def jieqcon(x, c=10):
""" Jacobian of Inequality constraint """
return array([[1, 1]])
# constraints dictionaries
cons = ({'type': 'eq', 'fun': feqcon, 'jac': jeqcon, 'args': (1, )},
{'type': 'ineq', 'fun': fieqcon, 'jac': jieqcon, 'args': (10,)})
# Bounds constraint problem
print(' Bounds constraints '.center(72, '-'))
print(' * fmin_slsqp')
x, f = fmin_slsqp(fun, array([-1, 1]), bounds=bnds, disp=1,
full_output=True)[:2]
print(' * _minimize_slsqp')
res = _minimize_slsqp(fun, array([-1, 1]), bounds=bnds,
**{'disp': True})
# Equality and inequality constraints problem
print(' Equality and inequality constraints '.center(72, '-'))
print(' * fmin_slsqp')
x, f = fmin_slsqp(fun, array([-1, 1]),
f_eqcons=feqcon, fprime_eqcons=jeqcon,
f_ieqcons=fieqcon, fprime_ieqcons=jieqcon,
disp=1, full_output=True)[:2]
print(' * _minimize_slsqp')
res = _minimize_slsqp(fun, array([-1, 1]), constraints=cons,
**{'disp': True})
| 18,568 | 35.409804 | 82 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_spectral.py
|
"""
Spectral Algorithm for Nonlinear Equations
"""
from __future__ import division, absolute_import, print_function
import collections
import numpy as np
from scipy.optimize import OptimizeResult
from scipy.optimize.optimize import _check_unknown_options
from .linesearch import _nonmonotone_line_search_cruz, _nonmonotone_line_search_cheng
class _NoConvergence(Exception):
pass
def _root_df_sane(func, x0, args=(), ftol=1e-8, fatol=1e-300, maxfev=1000,
fnorm=None, callback=None, disp=False, M=10, eta_strategy=None,
sigma_eps=1e-10, sigma_0=1.0, line_search='cruz', **unknown_options):
r"""
Solve nonlinear equation with the DF-SANE method
Options
-------
ftol : float, optional
Relative norm tolerance.
fatol : float, optional
Absolute norm tolerance.
Algorithm terminates when ``||func(x)|| < fatol + ftol ||func(x_0)||``.
fnorm : callable, optional
Norm to use in the convergence check. If None, 2-norm is used.
maxfev : int, optional
Maximum number of function evaluations.
disp : bool, optional
Whether to print convergence process to stdout.
eta_strategy : callable, optional
Choice of the ``eta_k`` parameter, which gives slack for growth
of ``||F||**2``. Called as ``eta_k = eta_strategy(k, x, F)`` with
`k` the iteration number, `x` the current iterate and `F` the current
residual. Should satisfy ``eta_k > 0`` and ``sum(eta, k=0..inf) < inf``.
Default: ``||F||**2 / (1 + k)**2``.
sigma_eps : float, optional
The spectral coefficient is constrained to ``sigma_eps < sigma < 1/sigma_eps``.
Default: 1e-10
sigma_0 : float, optional
Initial spectral coefficient.
Default: 1.0
M : int, optional
Number of iterates to include in the nonmonotonic line search.
Default: 10
line_search : {'cruz', 'cheng'}
Type of line search to employ. 'cruz' is the original one defined in
[Martinez & Raydan. Math. Comp. 75, 1429 (2006)], 'cheng' is
a modified search defined in [Cheng & Li. IMA J. Numer. Anal. 29, 814 (2009)].
Default: 'cruz'
References
----------
.. [1] "Spectral residual method without gradient information for solving
large-scale nonlinear systems of equations." W. La Cruz,
J.M. Martinez, M. Raydan. Math. Comp. **75**, 1429 (2006).
.. [2] W. La Cruz, Opt. Meth. Software, 29, 24 (2014).
.. [3] W. Cheng, D.-H. Li. IMA J. Numer. Anal. **29**, 814 (2009).
"""
_check_unknown_options(unknown_options)
if line_search not in ('cheng', 'cruz'):
raise ValueError("Invalid value %r for 'line_search'" % (line_search,))
nexp = 2
if eta_strategy is None:
# Different choice from [1], as their eta is not invariant
# vs. scaling of F.
def eta_strategy(k, x, F):
# Obtain squared 2-norm of the initial residual from the outer scope
return f_0 / (1 + k)**2
if fnorm is None:
def fnorm(F):
# Obtain squared 2-norm of the current residual from the outer scope
return f_k**(1.0/nexp)
def fmerit(F):
return np.linalg.norm(F)**nexp
nfev = [0]
f, x_k, x_shape, f_k, F_k, is_complex = _wrap_func(func, x0, fmerit, nfev, maxfev, args)
k = 0
f_0 = f_k
sigma_k = sigma_0
F_0_norm = fnorm(F_k)
# For the 'cruz' line search
prev_fs = collections.deque([f_k], M)
# For the 'cheng' line search
Q = 1.0
C = f_0
converged = False
message = "too many function evaluations required"
while True:
F_k_norm = fnorm(F_k)
if disp:
print("iter %d: ||F|| = %g, sigma = %g" % (k, F_k_norm, sigma_k))
if callback is not None:
callback(x_k, F_k)
if F_k_norm < ftol * F_0_norm + fatol:
# Converged!
message = "successful convergence"
converged = True
break
# Control spectral parameter, from [2]
if abs(sigma_k) > 1/sigma_eps:
sigma_k = 1/sigma_eps * np.sign(sigma_k)
elif abs(sigma_k) < sigma_eps:
sigma_k = sigma_eps
# Line search direction
d = -sigma_k * F_k
# Nonmonotone line search
eta = eta_strategy(k, x_k, F_k)
try:
if line_search == 'cruz':
alpha, xp, fp, Fp = _nonmonotone_line_search_cruz(f, x_k, d, prev_fs, eta=eta)
elif line_search == 'cheng':
alpha, xp, fp, Fp, C, Q = _nonmonotone_line_search_cheng(f, x_k, d, f_k, C, Q, eta=eta)
except _NoConvergence:
break
# Update spectral parameter
s_k = xp - x_k
y_k = Fp - F_k
sigma_k = np.vdot(s_k, s_k) / np.vdot(s_k, y_k)
# Take step
x_k = xp
F_k = Fp
f_k = fp
# Store function value
if line_search == 'cruz':
prev_fs.append(fp)
k += 1
x = _wrap_result(x_k, is_complex, shape=x_shape)
F = _wrap_result(F_k, is_complex)
result = OptimizeResult(x=x, success=converged,
message=message,
fun=F, nfev=nfev[0], nit=k)
return result
def _wrap_func(func, x0, fmerit, nfev_list, maxfev, args=()):
"""
Wrap a function and an initial value so that (i) complex values
are wrapped to reals, and (ii) value for a merit function
fmerit(x, f) is computed at the same time, (iii) iteration count
is maintained and an exception is raised if it is exceeded.
Parameters
----------
func : callable
Function to wrap
x0 : ndarray
Initial value
fmerit : callable
Merit function fmerit(f) for computing merit value from residual.
nfev_list : list
List to store number of evaluations in. Should be [0] in the beginning.
maxfev : int
Maximum number of evaluations before _NoConvergence is raised.
args : tuple
Extra arguments to func
Returns
-------
wrap_func : callable
Wrapped function, to be called as
``F, fp = wrap_func(x0)``
x0_wrap : ndarray of float
Wrapped initial value; raveled to 1D and complex
values mapped to reals.
x0_shape : tuple
Shape of the initial value array
f : float
Merit function at F
F : ndarray of float
Residual at x0_wrap
is_complex : bool
Whether complex values were mapped to reals
"""
x0 = np.asarray(x0)
x0_shape = x0.shape
F = np.asarray(func(x0, *args)).ravel()
is_complex = np.iscomplexobj(x0) or np.iscomplexobj(F)
x0 = x0.ravel()
nfev_list[0] = 1
if is_complex:
def wrap_func(x):
if nfev_list[0] >= maxfev:
raise _NoConvergence()
nfev_list[0] += 1
z = _real2complex(x).reshape(x0_shape)
v = np.asarray(func(z, *args)).ravel()
F = _complex2real(v)
f = fmerit(F)
return f, F
x0 = _complex2real(x0)
F = _complex2real(F)
else:
def wrap_func(x):
if nfev_list[0] >= maxfev:
raise _NoConvergence()
nfev_list[0] += 1
x = x.reshape(x0_shape)
F = np.asarray(func(x, *args)).ravel()
f = fmerit(F)
return f, F
return wrap_func, x0, x0_shape, fmerit(F), F, is_complex
def _wrap_result(result, is_complex, shape=None):
"""
Convert from real to complex and reshape result arrays.
"""
if is_complex:
z = _real2complex(result)
else:
z = result
if shape is not None:
z = z.reshape(shape)
return z
def _real2complex(x):
return np.ascontiguousarray(x, dtype=float).view(np.complex128)
def _complex2real(z):
return np.ascontiguousarray(z, dtype=complex).view(np.float64)
| 7,986 | 29.719231 | 103 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_remove_redundancy.py
|
"""
Routines for removing redundant (linearly dependent) equations from linear
programming equality constraints.
"""
# Author: Matt Haberland
from __future__ import division, print_function, absolute_import
import numpy as np
from scipy.linalg import svd
import scipy
def _row_count(A):
"""
Counts the number of nonzeros in each row of input array A.
Nonzeros are defined as any element with absolute value greater than
tol = 1e-13. This value should probably be an input to the function.
Parameters
----------
A : 2-D array
An array representing a matrix
Returns
-------
rowcount : 1-D array
Number of nonzeros in each row of A
"""
tol = 1e-13
return np.array((abs(A) > tol).sum(axis=1)).flatten()
def _get_densest(A, eligibleRows):
"""
Returns the index of the densest row of A. Ignores rows that are not
eligible for consideration.
Parameters
----------
A : 2-D array
An array representing a matrix
eligibleRows : 1-D logical array
Values indicate whether the corresponding row of A is eligible
to be considered
Returns
-------
i_densest : int
Index of the densest row in A eligible for consideration
"""
rowCounts = _row_count(A)
return np.argmax(rowCounts * eligibleRows)
def _remove_zero_rows(A, b):
"""
Eliminates trivial equations from system of equations defined by Ax = b
and identifies trivial infeasibilities
Parameters
----------
A : 2-D array
An array representing the left-hand side of a system of equations
b : 1-D array
An array representing the right-hand side of a system of equations
Returns
-------
A : 2-D array
An array representing the left-hand side of a system of equations
b : 1-D array
An array representing the right-hand side of a system of equations
status: int
An integer indicating the status of the removal operation
0: No infeasibility identified
2: Trivially infeasible
message : str
A string descriptor of the exit status of the optimization.
"""
status = 0
message = ""
i_zero = _row_count(A) == 0
A = A[np.logical_not(i_zero), :]
if not(np.allclose(b[i_zero], 0)):
status = 2
message = "There is a zero row in A_eq with a nonzero corresponding " \
"entry in b_eq. The problem is infeasible."
b = b[np.logical_not(i_zero)]
return A, b, status, message
def bg_update_dense(plu, perm_r, v, j):
LU, p = plu
u = scipy.linalg.solve_triangular(LU, v[perm_r], lower=True,
unit_diagonal=True)
LU[:j+1, j] = u[:j+1]
l = u[j+1:]
piv = LU[j, j]
LU[j+1:, j] += (l/piv)
return LU, p
def _remove_redundancy_dense(A, rhs):
"""
Eliminates redundant equations from system of equations defined by Ax = b
and identifies infeasibilities.
Parameters
----------
A : 2-D sparse matrix
An matrix representing the left-hand side of a system of equations
rhs : 1-D array
An array representing the right-hand side of a system of equations
Returns
----------
A : 2-D sparse matrix
A matrix representing the left-hand side of a system of equations
rhs : 1-D array
An array representing the right-hand side of a system of equations
status: int
An integer indicating the status of the system
0: No infeasibility identified
2: Trivially infeasible
message : str
A string descriptor of the exit status of the optimization.
References
----------
.. [2] Andersen, Erling D. "Finding all linearly dependent rows in
large-scale linear programming." Optimization Methods and Software
6.3 (1995): 219-227.
"""
tolapiv = 1e-8
tolprimal = 1e-8
status = 0
message = ""
inconsistent = ("There is a linear combination of rows of A_eq that "
"results in zero, suggesting a redundant constraint. "
"However the same linear combination of b_eq is "
"nonzero, suggesting that the constraints conflict "
"and the problem is infeasible.")
A, rhs, status, message = _remove_zero_rows(A, rhs)
if status != 0:
return A, rhs, status, message
m, n = A.shape
v = list(range(m)) # Artificial column indices.
b = list(v) # Basis column indices.
# This is better as a list than a set because column order of basis matrix
# needs to be consistent.
k = set(range(m, m+n)) # Structural column indices.
d = [] # Indices of dependent rows
lu = None
perm_r = None
A_orig = A
A = np.hstack((np.eye(m), A))
e = np.zeros(m)
# Implements basic algorithm from [2]
# Uses some of the suggested improvements (removing zero rows and
# Bartels-Golub update idea).
# Removing column singletons would be easy, but it is not as important
# because the procedure is performed only on the equality constraint
# matrix from the original problem - not on the canonical form matrix,
# which would have many more column singletons due to slack variables
# from the inequality constraints.
# The thoughts on "crashing" the initial basis sound useful, but the
# description of the procedure seems to assume a lot of familiarity with
# the subject; it is not very explicit. I already went through enough
# trouble getting the basic algorithm working, so I was not interested in
# trying to decipher this, too. (Overall, the paper is fraught with
# mistakes and ambiguities - which is strange, because the rest of
# Andersen's papers are quite good.)
B = A[:, b]
for i in v:
e[i] = 1
if i > 0:
e[i-1] = 0
try: # fails for i==0 and any time it gets ill-conditioned
j = b[i-1]
lu = bg_update_dense(lu, perm_r, A[:, j], i-1)
except:
lu = scipy.linalg.lu_factor(B)
LU, p = lu
perm_r = list(range(m))
for i1, i2 in enumerate(p):
perm_r[i1], perm_r[i2] = perm_r[i2], perm_r[i1]
pi = scipy.linalg.lu_solve(lu, e, trans=1)
# not efficient, but this is not the time sink...
js = np.array(list(k-set(b)))
batch = 50
dependent = True
# This is a tiny bit faster than looping over columns indivually,
# like for j in js: if abs(A[:,j].transpose().dot(pi)) > tolapiv:
for j_index in range(0, len(js), batch):
j_indices = js[np.arange(j_index, min(j_index+batch, len(js)))]
c = abs(A[:, j_indices].transpose().dot(pi))
if (c > tolapiv).any():
j = js[j_index + np.argmax(c)] # very independent column
B[:, i] = A[:, j]
b[i] = j
dependent = False
break
if dependent:
bibar = pi.T.dot(rhs.reshape(-1, 1))
bnorm = np.linalg.norm(rhs)
if abs(bibar)/(1+bnorm) > tolprimal: # inconsistent
status = 2
message = inconsistent
return A_orig, rhs, status, message
else: # dependent
d.append(i)
keep = set(range(m))
keep = list(keep - set(d))
return A_orig[keep, :], rhs[keep], status, message
def _remove_redundancy_sparse(A, rhs):
"""
Eliminates redundant equations from system of equations defined by Ax = b
and identifies infeasibilities.
Parameters
----------
A : 2-D sparse matrix
An matrix representing the left-hand side of a system of equations
rhs : 1-D array
An array representing the right-hand side of a system of equations
Returns
-------
A : 2-D sparse matrix
A matrix representing the left-hand side of a system of equations
rhs : 1-D array
An array representing the right-hand side of a system of equations
status: int
An integer indicating the status of the system
0: No infeasibility identified
2: Trivially infeasible
message : str
A string descriptor of the exit status of the optimization.
References
----------
.. [2] Andersen, Erling D. "Finding all linearly dependent rows in
large-scale linear programming." Optimization Methods and Software
6.3 (1995): 219-227.
"""
tolapiv = 1e-8
tolprimal = 1e-8
status = 0
message = ""
inconsistent = ("There is a linear combination of rows of A_eq that "
"results in zero, suggesting a redundant constraint. "
"However the same linear combination of b_eq is "
"nonzero, suggesting that the constraints conflict "
"and the problem is infeasible.")
A, rhs, status, message = _remove_zero_rows(A, rhs)
if status != 0:
return A, rhs, status, message
m, n = A.shape
v = list(range(m)) # Artificial column indices.
b = list(v) # Basis column indices.
# This is better as a list than a set because column order of basis matrix
# needs to be consistent.
k = set(range(m, m+n)) # Structural column indices.
d = [] # Indices of dependent rows
A_orig = A
A = scipy.sparse.hstack((scipy.sparse.eye(m), A)).tocsc()
e = np.zeros(m)
# Implements basic algorithm from [2]
# Uses only one of the suggested improvements (removing zero rows).
# Removing column singletons would be easy, but it is not as important
# because the procedure is performed only on the equality constraint
# matrix from the original problem - not on the canonical form matrix,
# which would have many more column singletons due to slack variables
# from the inequality constraints.
# The thoughts on "crashing" the initial basis sound useful, but the
# description of the procedure seems to assume a lot of familiarity with
# the subject; it is not very explicit. I already went through enough
# trouble getting the basic algorithm working, so I was not interested in
# trying to decipher this, too. (Overall, the paper is fraught with
# mistakes and ambiguities - which is strange, because the rest of
# Andersen's papers are quite good.)
# I tried and tried and tried to improve performance using the
# Bartels-Golub update. It works, but it's only practical if the LU
# factorization can be specialized as described, and that is not possible
# until the Scipy SuperLU interface permits control over column
# permutation - see issue #7700.
for i in v:
B = A[:, b]
e[i] = 1
if i > 0:
e[i-1] = 0
pi = scipy.sparse.linalg.spsolve(B.transpose(), e).reshape(-1, 1)
js = list(k-set(b)) # not efficient, but this is not the time sink...
# Due to overhead, it tends to be faster (for problems tested) to
# compute the full matrix-vector product rather than individual
# vector-vector products (with the chance of terminating as soon
# as any are nonzero). For very large matrices, it might be worth
# it to compute, say, 100 or 1000 at a time and stop when a nonzero
# is found.
c = (np.abs(A[:, js].transpose().dot(pi)) > tolapiv).nonzero()[0]
if len(c) > 0: # independent
j = js[c[0]]
# in a previous commit, the previous line was changed to choose
# index j corresponding with the maximum dot product.
# While this avoided issues with almost
# singular matrices, it slowed the routine in most NETLIB tests.
# I think this is because these columns were denser than the
# first column with nonzero dot product (c[0]).
# It would be nice to have a heuristic that balances sparsity with
# high dot product, but I don't think it's worth the time to
# develop one right now. Bartels-Golub update is a much higher
# priority.
b[i] = j # replace artificial column
else:
bibar = pi.T.dot(rhs.reshape(-1, 1))
bnorm = np.linalg.norm(rhs)
if abs(bibar)/(1 + bnorm) > tolprimal:
status = 2
message = inconsistent
return A_orig, rhs, status, message
else: # dependent
d.append(i)
keep = set(range(m))
keep = list(keep - set(d))
return A_orig[keep, :], rhs[keep], status, message
def _remove_redundancy(A, b):
"""
Eliminates redundant equations from system of equations defined by Ax = b
and identifies infeasibilities.
Parameters
----------
A : 2-D array
An array representing the left-hand side of a system of equations
b : 1-D array
An array representing the right-hand side of a system of equations
Returns
-------
A : 2-D array
An array representing the left-hand side of a system of equations
b : 1-D array
An array representing the right-hand side of a system of equations
status: int
An integer indicating the status of the system
0: No infeasibility identified
2: Trivially infeasible
message : str
A string descriptor of the exit status of the optimization.
References
----------
.. [2] Andersen, Erling D. "Finding all linearly dependent rows in
large-scale linear programming." Optimization Methods and Software
6.3 (1995): 219-227.
"""
A, b, status, message = _remove_zero_rows(A, b)
if status != 0:
return A, b, status, message
U, s, Vh = svd(A)
eps = np.finfo(float).eps
tol = s.max() * max(A.shape) * eps
m, n = A.shape
s_min = s[-1] if m <= n else 0
# this algorithm is faster than that of [2] when the nullspace is small
# but it could probably be improvement by randomized algorithms and with
# a sparse implementation.
# it relies on repeated singular value decomposition to find linearly
# dependent rows (as identified by columns of U that correspond with zero
# singular values). Unfortunately, only one row can be removed per
# decomposition (I tried otherwise; doing so can cause problems.)
# It would be nice if we could do truncated SVD like sp.sparse.linalg.svds
# but that function is unreliable at finding singular values near zero.
# Finding max eigenvalue L of A A^T, then largest eigenvalue (and
# associated eigenvector) of -A A^T + L I (I is identity) via power
# iteration would also work in theory, but is only efficient if the
# smallest nonzero eigenvalue of A A^T is close to the largest nonzero
# eigenvalue.
while abs(s_min) < tol:
v = U[:, -1] # TODO: return these so user can eliminate from problem?
# rows need to be represented in significant amount
eligibleRows = np.abs(v) > tol * 10e6
if not np.any(eligibleRows) or np.any(np.abs(v.dot(A)) > tol):
status = 4
message = ("Due to numerical issues, redundant equality "
"constraints could not be removed automatically. "
"Try providing your constraint matrices as sparse "
"matrices to activate sparse presolve, try turning "
"off redundancy removal, or try turning off presolve "
"altogether.")
break
if np.any(np.abs(v.dot(b)) > tol):
status = 2
message = ("There is a linear combination of rows of A_eq that "
"results in zero, suggesting a redundant constraint. "
"However the same linear combination of b_eq is "
"nonzero, suggesting that the constraints conflict "
"and the problem is infeasible.")
break
i_remove = _get_densest(A, eligibleRows)
A = np.delete(A, i_remove, axis=0)
b = np.delete(b, i_remove)
U, s, Vh = svd(A)
m, n = A.shape
s_min = s[-1] if m <= n else 0
return A, b, status, message
| 16,413 | 35.314159 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/__init__.py
|
"""
=====================================================
Optimization and root finding (:mod:`scipy.optimize`)
=====================================================
.. currentmodule:: scipy.optimize
Optimization
============
Local Optimization
------------------
.. autosummary::
:toctree: generated/
minimize - Interface for minimizers of multivariate functions
minimize_scalar - Interface for minimizers of univariate functions
OptimizeResult - The optimization result returned by some optimizers
OptimizeWarning - The optimization encountered problems
The `minimize` function supports the following methods:
.. toctree::
optimize.minimize-neldermead
optimize.minimize-powell
optimize.minimize-cg
optimize.minimize-bfgs
optimize.minimize-newtoncg
optimize.minimize-lbfgsb
optimize.minimize-tnc
optimize.minimize-cobyla
optimize.minimize-slsqp
optimize.minimize-trustconstr
optimize.minimize-dogleg
optimize.minimize-trustncg
optimize.minimize-trustkrylov
optimize.minimize-trustexact
Constraints are passed to `minimize` function as a single object or
as a list of objects from the following classes:
.. autosummary::
:toctree: generated/
NonlinearConstraint - Class defining general nonlinear constraints.
LinearConstraint - Class defining general linear constraints.
Simple bound constraints are handled separately and there is a special class
for them:
.. autosummary::
:toctree: generated/
Bounds - Bound constraints.
Quasi-Newton strategies implementing `HessianUpdateStrategy`
interface can be used to approximate the Hessian in `minimize`
function (available only for the 'trust-constr' method). Available
quasi-Newton methods implementing this interface are:
.. autosummary::
:toctree: generated/
BFGS - Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy.
SR1 - Symmetric-rank-1 Hessian update strategy.
The `minimize_scalar` function supports the following methods:
.. toctree::
optimize.minimize_scalar-brent
optimize.minimize_scalar-bounded
optimize.minimize_scalar-golden
The specific optimization method interfaces below in this subsection are
not recommended for use in new scripts; all of these methods are accessible
via a newer, more consistent interface provided by the functions above.
General-purpose multivariate methods:
.. autosummary::
:toctree: generated/
fmin - Nelder-Mead Simplex algorithm
fmin_powell - Powell's (modified) level set method
fmin_cg - Non-linear (Polak-Ribiere) conjugate gradient algorithm
fmin_bfgs - Quasi-Newton method (Broydon-Fletcher-Goldfarb-Shanno)
fmin_ncg - Line-search Newton Conjugate Gradient
Constrained multivariate methods:
.. autosummary::
:toctree: generated/
fmin_l_bfgs_b - Zhu, Byrd, and Nocedal's constrained optimizer
fmin_tnc - Truncated Newton code
fmin_cobyla - Constrained optimization by linear approximation
fmin_slsqp - Minimization using sequential least-squares programming
differential_evolution - stochastic minimization using differential evolution
Univariate (scalar) minimization methods:
.. autosummary::
:toctree: generated/
fminbound - Bounded minimization of a scalar function
brent - 1-D function minimization using Brent method
golden - 1-D function minimization using Golden Section method
Equation (Local) Minimizers
---------------------------
.. autosummary::
:toctree: generated/
leastsq - Minimize the sum of squares of M equations in N unknowns
least_squares - Feature-rich least-squares minimization.
nnls - Linear least-squares problem with non-negativity constraint
lsq_linear - Linear least-squares problem with bound constraints
Global Optimization
-------------------
.. autosummary::
:toctree: generated/
basinhopping - Basinhopping stochastic optimizer
brute - Brute force searching optimizer
differential_evolution - stochastic minimization using differential evolution
Rosenbrock function
-------------------
.. autosummary::
:toctree: generated/
rosen - The Rosenbrock function.
rosen_der - The derivative of the Rosenbrock function.
rosen_hess - The Hessian matrix of the Rosenbrock function.
rosen_hess_prod - Product of the Rosenbrock Hessian with a vector.
Fitting
=======
.. autosummary::
:toctree: generated/
curve_fit -- Fit curve to a set of points
Root finding
============
Scalar functions
----------------
.. autosummary::
:toctree: generated/
brentq - quadratic interpolation Brent method
brenth - Brent method, modified by Harris with hyperbolic extrapolation
ridder - Ridder's method
bisect - Bisection method
newton - Secant method or Newton's method
Fixed point finding:
.. autosummary::
:toctree: generated/
fixed_point - Single-variable fixed-point solver
Multidimensional
----------------
General nonlinear solvers:
.. autosummary::
:toctree: generated/
root - Unified interface for nonlinear solvers of multivariate functions
fsolve - Non-linear multi-variable equation solver
broyden1 - Broyden's first method
broyden2 - Broyden's second method
The `root` function supports the following methods:
.. toctree::
optimize.root-hybr
optimize.root-lm
optimize.root-broyden1
optimize.root-broyden2
optimize.root-anderson
optimize.root-linearmixing
optimize.root-diagbroyden
optimize.root-excitingmixing
optimize.root-krylov
optimize.root-dfsane
Large-scale nonlinear solvers:
.. autosummary::
:toctree: generated/
newton_krylov
anderson
Simple iterations:
.. autosummary::
:toctree: generated/
excitingmixing
linearmixing
diagbroyden
:mod:`Additional information on the nonlinear solvers <scipy.optimize.nonlin>`
Linear Programming
==================
General linear programming solver:
.. autosummary::
:toctree: generated/
linprog -- Unified interface for minimizers of linear programming problems
The `linprog` function supports the following methods:
.. toctree::
optimize.linprog-simplex
optimize.linprog-interior-point
The simplex method supports callback functions, such as:
.. autosummary::
:toctree: generated/
linprog_verbose_callback -- Sample callback function for linprog (simplex)
Assignment problems:
.. autosummary::
:toctree: generated/
linear_sum_assignment -- Solves the linear-sum assignment problem
Utilities
=========
.. autosummary::
:toctree: generated/
approx_fprime - Approximate the gradient of a scalar function
bracket - Bracket a minimum, given two starting points
check_grad - Check the supplied derivative using finite differences
line_search - Return a step that satisfies the strong Wolfe conditions
show_options - Show specific options optimization solvers
LbfgsInvHessProduct - Linear operator for L-BFGS approximate inverse Hessian
HessianUpdateStrategy - Interface for implementing Hessian update strategies
"""
from __future__ import division, print_function, absolute_import
from .optimize import *
from ._minimize import *
from ._root import *
from .minpack import *
from .zeros import *
from .lbfgsb import fmin_l_bfgs_b, LbfgsInvHessProduct
from .tnc import fmin_tnc
from .cobyla import fmin_cobyla
from .nonlin import *
from .slsqp import fmin_slsqp
from .nnls import nnls
from ._basinhopping import basinhopping
from ._linprog import linprog, linprog_verbose_callback
from ._hungarian import linear_sum_assignment
from ._differentialevolution import differential_evolution
from ._lsq import least_squares, lsq_linear
from ._constraints import (NonlinearConstraint,
LinearConstraint,
Bounds)
from ._hessian_update_strategy import HessianUpdateStrategy, BFGS, SR1
__all__ = [s for s in dir() if not s.startswith('_')]
from scipy._lib._testutils import PytestTester
test = PytestTester(__name__)
del PytestTester
| 7,953 | 25.871622 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/minpack.py
|
from __future__ import division, print_function, absolute_import
import threading
import warnings
from . import _minpack
import numpy as np
from numpy import (atleast_1d, dot, take, triu, shape, eye,
transpose, zeros, product, greater, array,
all, where, isscalar, asarray, inf, abs,
finfo, inexact, issubdtype, dtype)
from scipy.linalg import svd, cholesky, solve_triangular, LinAlgError
from scipy._lib._util import _asarray_validated, _lazywhere
from .optimize import OptimizeResult, _check_unknown_options, OptimizeWarning
from ._lsq import least_squares
from ._lsq.common import make_strictly_feasible
from ._lsq.least_squares import prepare_bounds
_MINPACK_LOCK = threading.RLock()
error = _minpack.error
__all__ = ['fsolve', 'leastsq', 'fixed_point', 'curve_fit']
def _check_func(checker, argname, thefunc, x0, args, numinputs,
output_shape=None):
res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
if (output_shape is not None) and (shape(res) != output_shape):
if (output_shape[0] != 1):
if len(output_shape) > 1:
if output_shape[1] == 1:
return shape(res)
msg = "%s: there is a mismatch between the input and output " \
"shape of the '%s' argument" % (checker, argname)
func_name = getattr(thefunc, '__name__', None)
if func_name:
msg += " '%s'." % func_name
else:
msg += "."
msg += 'Shape should be %s but it is %s.' % (output_shape, shape(res))
raise TypeError(msg)
if issubdtype(res.dtype, inexact):
dt = res.dtype
else:
dt = dtype(float)
return shape(res), dt
def fsolve(func, x0, args=(), fprime=None, full_output=0,
col_deriv=0, xtol=1.49012e-8, maxfev=0, band=None,
epsfcn=None, factor=100, diag=None):
"""
Find the roots of a function.
Return the roots of the (non-linear) equations defined by
``func(x) = 0`` given a starting estimate.
Parameters
----------
func : callable ``f(x, *args)``
A function that takes at least one (possibly vector) argument,
and returns a value of the same length.
x0 : ndarray
The starting estimate for the roots of ``func(x) = 0``.
args : tuple, optional
Any extra arguments to `func`.
fprime : callable ``f(x, *args)``, optional
A function to compute the Jacobian of `func` with derivatives
across the rows. By default, the Jacobian will be estimated.
full_output : bool, optional
If True, return optional outputs.
col_deriv : bool, optional
Specify whether the Jacobian function computes derivatives down
the columns (faster, because there is no transpose operation).
xtol : float, optional
The calculation will terminate if the relative error between two
consecutive iterates is at most `xtol`.
maxfev : int, optional
The maximum number of calls to the function. If zero, then
``100*(N+1)`` is the maximum where N is the number of elements
in `x0`.
band : tuple, optional
If set to a two-sequence containing the number of sub- and
super-diagonals within the band of the Jacobi matrix, the
Jacobi matrix is considered banded (only for ``fprime=None``).
epsfcn : float, optional
A suitable step length for the forward-difference
approximation of the Jacobian (for ``fprime=None``). If
`epsfcn` is less than the machine precision, it is assumed
that the relative errors in the functions are of the order of
the machine precision.
factor : float, optional
A parameter determining the initial step bound
(``factor * || diag * x||``). Should be in the interval
``(0.1, 100)``.
diag : sequence, optional
N positive entries that serve as a scale factors for the
variables.
Returns
-------
x : ndarray
The solution (or the result of the last iteration for
an unsuccessful call).
infodict : dict
A dictionary of optional outputs with the keys:
``nfev``
number of function calls
``njev``
number of Jacobian calls
``fvec``
function evaluated at the output
``fjac``
the orthogonal matrix, q, produced by the QR
factorization of the final approximate Jacobian
matrix, stored column wise
``r``
upper triangular matrix produced by QR factorization
of the same matrix
``qtf``
the vector ``(transpose(q) * fvec)``
ier : int
An integer flag. Set to 1 if a solution was found, otherwise refer
to `mesg` for more information.
mesg : str
If no solution is found, `mesg` details the cause of failure.
See Also
--------
root : Interface to root finding algorithms for multivariate
functions. See the 'hybr' `method` in particular.
Notes
-----
``fsolve`` is a wrapper around MINPACK's hybrd and hybrj algorithms.
"""
options = {'col_deriv': col_deriv,
'xtol': xtol,
'maxfev': maxfev,
'band': band,
'eps': epsfcn,
'factor': factor,
'diag': diag}
res = _root_hybr(func, x0, args, jac=fprime, **options)
if full_output:
x = res['x']
info = dict((k, res.get(k))
for k in ('nfev', 'njev', 'fjac', 'r', 'qtf') if k in res)
info['fvec'] = res['fun']
return x, info, res['status'], res['message']
else:
status = res['status']
msg = res['message']
if status == 0:
raise TypeError(msg)
elif status == 1:
pass
elif status in [2, 3, 4, 5]:
warnings.warn(msg, RuntimeWarning)
else:
raise TypeError(msg)
return res['x']
def _root_hybr(func, x0, args=(), jac=None,
col_deriv=0, xtol=1.49012e-08, maxfev=0, band=None, eps=None,
factor=100, diag=None, **unknown_options):
"""
Find the roots of a multivariate function using MINPACK's hybrd and
hybrj routines (modified Powell method).
Options
-------
col_deriv : bool
Specify whether the Jacobian function computes derivatives down
the columns (faster, because there is no transpose operation).
xtol : float
The calculation will terminate if the relative error between two
consecutive iterates is at most `xtol`.
maxfev : int
The maximum number of calls to the function. If zero, then
``100*(N+1)`` is the maximum where N is the number of elements
in `x0`.
band : tuple
If set to a two-sequence containing the number of sub- and
super-diagonals within the band of the Jacobi matrix, the
Jacobi matrix is considered banded (only for ``fprime=None``).
eps : float
A suitable step length for the forward-difference
approximation of the Jacobian (for ``fprime=None``). If
`eps` is less than the machine precision, it is assumed
that the relative errors in the functions are of the order of
the machine precision.
factor : float
A parameter determining the initial step bound
(``factor * || diag * x||``). Should be in the interval
``(0.1, 100)``.
diag : sequence
N positive entries that serve as a scale factors for the
variables.
"""
_check_unknown_options(unknown_options)
epsfcn = eps
x0 = asarray(x0).flatten()
n = len(x0)
if not isinstance(args, tuple):
args = (args,)
shape, dtype = _check_func('fsolve', 'func', func, x0, args, n, (n,))
if epsfcn is None:
epsfcn = finfo(dtype).eps
Dfun = jac
if Dfun is None:
if band is None:
ml, mu = -10, -10
else:
ml, mu = band[:2]
if maxfev == 0:
maxfev = 200 * (n + 1)
with _MINPACK_LOCK:
retval = _minpack._hybrd(func, x0, args, 1, xtol, maxfev,
ml, mu, epsfcn, factor, diag)
else:
_check_func('fsolve', 'fprime', Dfun, x0, args, n, (n, n))
if (maxfev == 0):
maxfev = 100 * (n + 1)
with _MINPACK_LOCK:
retval = _minpack._hybrj(func, Dfun, x0, args, 1,
col_deriv, xtol, maxfev, factor, diag)
x, status = retval[0], retval[-1]
errors = {0: "Improper input parameters were entered.",
1: "The solution converged.",
2: "The number of calls to function has "
"reached maxfev = %d." % maxfev,
3: "xtol=%f is too small, no further improvement "
"in the approximate\n solution "
"is possible." % xtol,
4: "The iteration is not making good progress, as measured "
"by the \n improvement from the last five "
"Jacobian evaluations.",
5: "The iteration is not making good progress, "
"as measured by the \n improvement from the last "
"ten iterations.",
'unknown': "An error occurred."}
info = retval[1]
info['fun'] = info.pop('fvec')
sol = OptimizeResult(x=x, success=(status == 1), status=status)
sol.update(info)
try:
sol['message'] = errors[status]
except KeyError:
sol['message'] = errors['unknown']
return sol
def leastsq(func, x0, args=(), Dfun=None, full_output=0,
col_deriv=0, ftol=1.49012e-8, xtol=1.49012e-8,
gtol=0.0, maxfev=0, epsfcn=None, factor=100, diag=None):
"""
Minimize the sum of squares of a set of equations.
::
x = arg min(sum(func(y)**2,axis=0))
y
Parameters
----------
func : callable
should take at least one (possibly length N vector) argument and
returns M floating point numbers. It must not return NaNs or
fitting might fail.
x0 : ndarray
The starting estimate for the minimization.
args : tuple, optional
Any extra arguments to func are placed in this tuple.
Dfun : callable, optional
A function or method to compute the Jacobian of func with derivatives
across the rows. If this is None, the Jacobian will be estimated.
full_output : bool, optional
non-zero to return all optional outputs.
col_deriv : bool, optional
non-zero to specify that the Jacobian function computes derivatives
down the columns (faster, because there is no transpose operation).
ftol : float, optional
Relative error desired in the sum of squares.
xtol : float, optional
Relative error desired in the approximate solution.
gtol : float, optional
Orthogonality desired between the function vector and the columns of
the Jacobian.
maxfev : int, optional
The maximum number of calls to the function. If `Dfun` is provided
then the default `maxfev` is 100*(N+1) where N is the number of elements
in x0, otherwise the default `maxfev` is 200*(N+1).
epsfcn : float, optional
A variable used in determining a suitable step length for the forward-
difference approximation of the Jacobian (for Dfun=None).
Normally the actual step length will be sqrt(epsfcn)*x
If epsfcn is less than the machine precision, it is assumed that the
relative errors are of the order of the machine precision.
factor : float, optional
A parameter determining the initial step bound
(``factor * || diag * x||``). Should be in interval ``(0.1, 100)``.
diag : sequence, optional
N positive entries that serve as a scale factors for the variables.
Returns
-------
x : ndarray
The solution (or the result of the last iteration for an unsuccessful
call).
cov_x : ndarray
Uses the fjac and ipvt optional outputs to construct an
estimate of the jacobian around the solution. None if a
singular matrix encountered (indicates very flat curvature in
some direction). This matrix must be multiplied by the
residual variance to get the covariance of the
parameter estimates -- see curve_fit.
infodict : dict
a dictionary of optional outputs with the key s:
``nfev``
The number of function calls
``fvec``
The function evaluated at the output
``fjac``
A permutation of the R matrix of a QR
factorization of the final approximate
Jacobian matrix, stored column wise.
Together with ipvt, the covariance of the
estimate can be approximated.
``ipvt``
An integer array of length N which defines
a permutation matrix, p, such that
fjac*p = q*r, where r is upper triangular
with diagonal elements of nonincreasing
magnitude. Column j of p is column ipvt(j)
of the identity matrix.
``qtf``
The vector (transpose(q) * fvec).
mesg : str
A string message giving information about the cause of failure.
ier : int
An integer flag. If it is equal to 1, 2, 3 or 4, the solution was
found. Otherwise, the solution was not found. In either case, the
optional output variable 'mesg' gives more information.
Notes
-----
"leastsq" is a wrapper around MINPACK's lmdif and lmder algorithms.
cov_x is a Jacobian approximation to the Hessian of the least squares
objective function.
This approximation assumes that the objective function is based on the
difference between some observed target data (ydata) and a (non-linear)
function of the parameters `f(xdata, params)` ::
func(params) = ydata - f(xdata, params)
so that the objective function is ::
min sum((ydata - f(xdata, params))**2, axis=0)
params
The solution, `x`, is always a 1D array, regardless of the shape of `x0`,
or whether `x0` is a scalar.
"""
x0 = asarray(x0).flatten()
n = len(x0)
if not isinstance(args, tuple):
args = (args,)
shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
m = shape[0]
if n > m:
raise TypeError('Improper input: N=%s must not exceed M=%s' % (n, m))
if epsfcn is None:
epsfcn = finfo(dtype).eps
if Dfun is None:
if maxfev == 0:
maxfev = 200*(n + 1)
with _MINPACK_LOCK:
retval = _minpack._lmdif(func, x0, args, full_output, ftol, xtol,
gtol, maxfev, epsfcn, factor, diag)
else:
if col_deriv:
_check_func('leastsq', 'Dfun', Dfun, x0, args, n, (n, m))
else:
_check_func('leastsq', 'Dfun', Dfun, x0, args, n, (m, n))
if maxfev == 0:
maxfev = 100 * (n + 1)
with _MINPACK_LOCK:
retval = _minpack._lmder(func, Dfun, x0, args, full_output,
col_deriv, ftol, xtol, gtol, maxfev,
factor, diag)
errors = {0: ["Improper input parameters.", TypeError],
1: ["Both actual and predicted relative reductions "
"in the sum of squares\n are at most %f" % ftol, None],
2: ["The relative error between two consecutive "
"iterates is at most %f" % xtol, None],
3: ["Both actual and predicted relative reductions in "
"the sum of squares\n are at most %f and the "
"relative error between two consecutive "
"iterates is at \n most %f" % (ftol, xtol), None],
4: ["The cosine of the angle between func(x) and any "
"column of the\n Jacobian is at most %f in "
"absolute value" % gtol, None],
5: ["Number of calls to function has reached "
"maxfev = %d." % maxfev, ValueError],
6: ["ftol=%f is too small, no further reduction "
"in the sum of squares\n is possible.""" % ftol,
ValueError],
7: ["xtol=%f is too small, no further improvement in "
"the approximate\n solution is possible." % xtol,
ValueError],
8: ["gtol=%f is too small, func(x) is orthogonal to the "
"columns of\n the Jacobian to machine "
"precision." % gtol, ValueError],
'unknown': ["Unknown error.", TypeError]}
info = retval[-1] # The FORTRAN return value
if info not in [1, 2, 3, 4] and not full_output:
if info in [5, 6, 7, 8]:
warnings.warn(errors[info][0], RuntimeWarning)
else:
try:
raise errors[info][1](errors[info][0])
except KeyError:
raise errors['unknown'][1](errors['unknown'][0])
mesg = errors[info][0]
if full_output:
cov_x = None
if info in [1, 2, 3, 4]:
from numpy.dual import inv
perm = take(eye(n), retval[1]['ipvt'] - 1, 0)
r = triu(transpose(retval[1]['fjac'])[:n, :])
R = dot(r, perm)
try:
cov_x = inv(dot(transpose(R), R))
except (LinAlgError, ValueError):
pass
return (retval[0], cov_x) + retval[1:-1] + (mesg, info)
else:
return (retval[0], info)
def _wrap_func(func, xdata, ydata, transform):
if transform is None:
def func_wrapped(params):
return func(xdata, *params) - ydata
elif transform.ndim == 1:
def func_wrapped(params):
return transform * (func(xdata, *params) - ydata)
else:
# Chisq = (y - yd)^T C^{-1} (y-yd)
# transform = L such that C = L L^T
# C^{-1} = L^{-T} L^{-1}
# Chisq = (y - yd)^T L^{-T} L^{-1} (y-yd)
# Define (y-yd)' = L^{-1} (y-yd)
# by solving
# L (y-yd)' = (y-yd)
# and minimize (y-yd)'^T (y-yd)'
def func_wrapped(params):
return solve_triangular(transform, func(xdata, *params) - ydata, lower=True)
return func_wrapped
def _wrap_jac(jac, xdata, transform):
if transform is None:
def jac_wrapped(params):
return jac(xdata, *params)
elif transform.ndim == 1:
def jac_wrapped(params):
return transform[:, np.newaxis] * np.asarray(jac(xdata, *params))
else:
def jac_wrapped(params):
return solve_triangular(transform, np.asarray(jac(xdata, *params)), lower=True)
return jac_wrapped
def _initialize_feasible(lb, ub):
p0 = np.ones_like(lb)
lb_finite = np.isfinite(lb)
ub_finite = np.isfinite(ub)
mask = lb_finite & ub_finite
p0[mask] = 0.5 * (lb[mask] + ub[mask])
mask = lb_finite & ~ub_finite
p0[mask] = lb[mask] + 1
mask = ~lb_finite & ub_finite
p0[mask] = ub[mask] - 1
return p0
def curve_fit(f, xdata, ydata, p0=None, sigma=None, absolute_sigma=False,
check_finite=True, bounds=(-np.inf, np.inf), method=None,
jac=None, **kwargs):
"""
Use non-linear least squares to fit a function, f, to data.
Assumes ``ydata = f(xdata, *params) + eps``
Parameters
----------
f : callable
The model function, f(x, ...). It must take the independent
variable as the first argument and the parameters to fit as
separate remaining arguments.
xdata : An M-length sequence or an (k,M)-shaped array for functions with k predictors
The independent variable where the data is measured.
ydata : M-length sequence
The dependent data --- nominally f(xdata, ...)
p0 : None, scalar, or N-length sequence, optional
Initial guess for the parameters. If None, then the initial
values will all be 1 (if the number of parameters for the function
can be determined using introspection, otherwise a ValueError
is raised).
sigma : None or M-length sequence or MxM array, optional
Determines the uncertainty in `ydata`. If we define residuals as
``r = ydata - f(xdata, *popt)``, then the interpretation of `sigma`
depends on its number of dimensions:
- A 1-d `sigma` should contain values of standard deviations of
errors in `ydata`. In this case, the optimized function is
``chisq = sum((r / sigma) ** 2)``.
- A 2-d `sigma` should contain the covariance matrix of
errors in `ydata`. In this case, the optimized function is
``chisq = r.T @ inv(sigma) @ r``.
.. versionadded:: 0.19
None (default) is equivalent of 1-d `sigma` filled with ones.
absolute_sigma : bool, optional
If True, `sigma` is used in an absolute sense and the estimated parameter
covariance `pcov` reflects these absolute values.
If False, only the relative magnitudes of the `sigma` values matter.
The returned parameter covariance matrix `pcov` is based on scaling
`sigma` by a constant factor. This constant is set by demanding that the
reduced `chisq` for the optimal parameters `popt` when using the
*scaled* `sigma` equals unity. In other words, `sigma` is scaled to
match the sample variance of the residuals after the fit.
Mathematically,
``pcov(absolute_sigma=False) = pcov(absolute_sigma=True) * chisq(popt)/(M-N)``
check_finite : bool, optional
If True, check that the input arrays do not contain nans of infs,
and raise a ValueError if they do. Setting this parameter to
False may silently produce nonsensical results if the input arrays
do contain nans. Default is True.
bounds : 2-tuple of array_like, optional
Lower and upper bounds on parameters. Defaults to no bounds.
Each element of the tuple must be either an array with the length equal
to the number of parameters, or a scalar (in which case the bound is
taken to be the same for all parameters.) Use ``np.inf`` with an
appropriate sign to disable bounds on all or some parameters.
.. versionadded:: 0.17
method : {'lm', 'trf', 'dogbox'}, optional
Method to use for optimization. See `least_squares` for more details.
Default is 'lm' for unconstrained problems and 'trf' if `bounds` are
provided. The method 'lm' won't work when the number of observations
is less than the number of variables, use 'trf' or 'dogbox' in this
case.
.. versionadded:: 0.17
jac : callable, string or None, optional
Function with signature ``jac(x, ...)`` which computes the Jacobian
matrix of the model function with respect to parameters as a dense
array_like structure. It will be scaled according to provided `sigma`.
If None (default), the Jacobian will be estimated numerically.
String keywords for 'trf' and 'dogbox' methods can be used to select
a finite difference scheme, see `least_squares`.
.. versionadded:: 0.18
kwargs
Keyword arguments passed to `leastsq` for ``method='lm'`` or
`least_squares` otherwise.
Returns
-------
popt : array
Optimal values for the parameters so that the sum of the squared
residuals of ``f(xdata, *popt) - ydata`` is minimized
pcov : 2d array
The estimated covariance of popt. The diagonals provide the variance
of the parameter estimate. To compute one standard deviation errors
on the parameters use ``perr = np.sqrt(np.diag(pcov))``.
How the `sigma` parameter affects the estimated covariance
depends on `absolute_sigma` argument, as described above.
If the Jacobian matrix at the solution doesn't have a full rank, then
'lm' method returns a matrix filled with ``np.inf``, on the other hand
'trf' and 'dogbox' methods use Moore-Penrose pseudoinverse to compute
the covariance matrix.
Raises
------
ValueError
if either `ydata` or `xdata` contain NaNs, or if incompatible options
are used.
RuntimeError
if the least-squares minimization fails.
OptimizeWarning
if covariance of the parameters can not be estimated.
See Also
--------
least_squares : Minimize the sum of squares of nonlinear functions.
scipy.stats.linregress : Calculate a linear least squares regression for
two sets of measurements.
Notes
-----
With ``method='lm'``, the algorithm uses the Levenberg-Marquardt algorithm
through `leastsq`. Note that this algorithm can only deal with
unconstrained problems.
Box constraints can be handled by methods 'trf' and 'dogbox'. Refer to
the docstring of `least_squares` for more information.
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.optimize import curve_fit
>>> def func(x, a, b, c):
... return a * np.exp(-b * x) + c
Define the data to be fit with some noise:
>>> xdata = np.linspace(0, 4, 50)
>>> y = func(xdata, 2.5, 1.3, 0.5)
>>> np.random.seed(1729)
>>> y_noise = 0.2 * np.random.normal(size=xdata.size)
>>> ydata = y + y_noise
>>> plt.plot(xdata, ydata, 'b-', label='data')
Fit for the parameters a, b, c of the function `func`:
>>> popt, pcov = curve_fit(func, xdata, ydata)
>>> popt
array([ 2.55423706, 1.35190947, 0.47450618])
>>> plt.plot(xdata, func(xdata, *popt), 'r-',
... label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
Constrain the optimization to the region of ``0 <= a <= 3``,
``0 <= b <= 1`` and ``0 <= c <= 0.5``:
>>> popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 1., 0.5]))
>>> popt
array([ 2.43708906, 1. , 0.35015434])
>>> plt.plot(xdata, func(xdata, *popt), 'g--',
... label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
>>> plt.xlabel('x')
>>> plt.ylabel('y')
>>> plt.legend()
>>> plt.show()
"""
if p0 is None:
# determine number of parameters by inspecting the function
from scipy._lib._util import getargspec_no_self as _getargspec
args, varargs, varkw, defaults = _getargspec(f)
if len(args) < 2:
raise ValueError("Unable to determine number of fit parameters.")
n = len(args) - 1
else:
p0 = np.atleast_1d(p0)
n = p0.size
lb, ub = prepare_bounds(bounds, n)
if p0 is None:
p0 = _initialize_feasible(lb, ub)
bounded_problem = np.any((lb > -np.inf) | (ub < np.inf))
if method is None:
if bounded_problem:
method = 'trf'
else:
method = 'lm'
if method == 'lm' and bounded_problem:
raise ValueError("Method 'lm' only works for unconstrained problems. "
"Use 'trf' or 'dogbox' instead.")
# NaNs can not be handled
if check_finite:
ydata = np.asarray_chkfinite(ydata)
else:
ydata = np.asarray(ydata)
if isinstance(xdata, (list, tuple, np.ndarray)):
# `xdata` is passed straight to the user-defined `f`, so allow
# non-array_like `xdata`.
if check_finite:
xdata = np.asarray_chkfinite(xdata)
else:
xdata = np.asarray(xdata)
# Determine type of sigma
if sigma is not None:
sigma = np.asarray(sigma)
# if 1-d, sigma are errors, define transform = 1/sigma
if sigma.shape == (ydata.size, ):
transform = 1.0 / sigma
# if 2-d, sigma is the covariance matrix,
# define transform = L such that L L^T = C
elif sigma.shape == (ydata.size, ydata.size):
try:
# scipy.linalg.cholesky requires lower=True to return L L^T = A
transform = cholesky(sigma, lower=True)
except LinAlgError:
raise ValueError("`sigma` must be positive definite.")
else:
raise ValueError("`sigma` has incorrect shape.")
else:
transform = None
func = _wrap_func(f, xdata, ydata, transform)
if callable(jac):
jac = _wrap_jac(jac, xdata, transform)
elif jac is None and method != 'lm':
jac = '2-point'
if method == 'lm':
# Remove full_output from kwargs, otherwise we're passing it in twice.
return_full = kwargs.pop('full_output', False)
res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
popt, pcov, infodict, errmsg, ier = res
cost = np.sum(infodict['fvec'] ** 2)
if ier not in [1, 2, 3, 4]:
raise RuntimeError("Optimal parameters not found: " + errmsg)
else:
# Rename maxfev (leastsq) to max_nfev (least_squares), if specified.
if 'max_nfev' not in kwargs:
kwargs['max_nfev'] = kwargs.pop('maxfev', None)
res = least_squares(func, p0, jac=jac, bounds=bounds, method=method,
**kwargs)
if not res.success:
raise RuntimeError("Optimal parameters not found: " + res.message)
cost = 2 * res.cost # res.cost is half sum of squares!
popt = res.x
# Do Moore-Penrose inverse discarding zero singular values.
_, s, VT = svd(res.jac, full_matrices=False)
threshold = np.finfo(float).eps * max(res.jac.shape) * s[0]
s = s[s > threshold]
VT = VT[:s.size]
pcov = np.dot(VT.T / s**2, VT)
return_full = False
warn_cov = False
if pcov is None:
# indeterminate covariance
pcov = zeros((len(popt), len(popt)), dtype=float)
pcov.fill(inf)
warn_cov = True
elif not absolute_sigma:
if ydata.size > p0.size:
s_sq = cost / (ydata.size - p0.size)
pcov = pcov * s_sq
else:
pcov.fill(inf)
warn_cov = True
if warn_cov:
warnings.warn('Covariance of the parameters could not be estimated',
category=OptimizeWarning)
if return_full:
return popt, pcov, infodict, errmsg, ier
else:
return popt, pcov
def check_gradient(fcn, Dfcn, x0, args=(), col_deriv=0):
"""Perform a simple check on the gradient for correctness.
"""
x = atleast_1d(x0)
n = len(x)
x = x.reshape((n,))
fvec = atleast_1d(fcn(x, *args))
m = len(fvec)
fvec = fvec.reshape((m,))
ldfjac = m
fjac = atleast_1d(Dfcn(x, *args))
fjac = fjac.reshape((m, n))
if col_deriv == 0:
fjac = transpose(fjac)
xp = zeros((n,), float)
err = zeros((m,), float)
fvecp = None
with _MINPACK_LOCK:
_minpack._chkder(m, n, x, fvec, fjac, ldfjac, xp, fvecp, 1, err)
fvecp = atleast_1d(fcn(xp, *args))
fvecp = fvecp.reshape((m,))
with _MINPACK_LOCK:
_minpack._chkder(m, n, x, fvec, fjac, ldfjac, xp, fvecp, 2, err)
good = (product(greater(err, 0.5), axis=0))
return (good, err)
def _del2(p0, p1, d):
return p0 - np.square(p1 - p0) / d
def _relerr(actual, desired):
return (actual - desired) / desired
def _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel):
p0 = x0
for i in range(maxiter):
p1 = func(p0, *args)
if use_accel:
p2 = func(p1, *args)
d = p2 - 2.0 * p1 + p0
p = _lazywhere(d != 0, (p0, p1, d), f=_del2, fillvalue=p2)
else:
p = p1
relerr = _lazywhere(p0 != 0, (p, p0), f=_relerr, fillvalue=p)
if np.all(np.abs(relerr) < xtol):
return p
p0 = p
msg = "Failed to converge after %d iterations, value is %s" % (maxiter, p)
raise RuntimeError(msg)
def fixed_point(func, x0, args=(), xtol=1e-8, maxiter=500, method='del2'):
"""
Find a fixed point of the function.
Given a function of one or more variables and a starting point, find a
fixed-point of the function: i.e. where ``func(x0) == x0``.
Parameters
----------
func : function
Function to evaluate.
x0 : array_like
Fixed point of function.
args : tuple, optional
Extra arguments to `func`.
xtol : float, optional
Convergence tolerance, defaults to 1e-08.
maxiter : int, optional
Maximum number of iterations, defaults to 500.
method : {"del2", "iteration"}, optional
Method of finding the fixed-point, defaults to "del2"
which uses Steffensen's Method with Aitken's ``Del^2``
convergence acceleration [1]_. The "iteration" method simply iterates
the function until convergence is detected, without attempting to
accelerate the convergence.
References
----------
.. [1] Burden, Faires, "Numerical Analysis", 5th edition, pg. 80
Examples
--------
>>> from scipy import optimize
>>> def func(x, c1, c2):
... return np.sqrt(c1/(x+c2))
>>> c1 = np.array([10,12.])
>>> c2 = np.array([3, 5.])
>>> optimize.fixed_point(func, [1.2, 1.3], args=(c1,c2))
array([ 1.4920333 , 1.37228132])
"""
use_accel = {'del2': True, 'iteration': False}[method]
x0 = _asarray_validated(x0, as_inexact=True)
return _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel)
| 33,844 | 36.39779 | 91 |
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cba-pipeline-public
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_constraints.py
|
"""Constraints definition for minimize."""
from __future__ import division, print_function, absolute_import
import numpy as np
from ._hessian_update_strategy import BFGS
from ._differentiable_functions import (
VectorFunction, LinearVectorFunction, IdentityVectorFunction)
class NonlinearConstraint(object):
"""Nonlinear constraint on the variables.
The constraint has the general inequality form::
lb <= fun(x) <= ub
Here the vector of independent variables x is passed as ndarray of shape
(n,) and ``fun`` returns a vector with m components.
It is possible to use equal bounds to represent an equality constraint or
infinite bounds to represent a one-sided constraint.
Parameters
----------
fun : callable
The function defining the constraint.
The signature is ``fun(x) -> array_like, shape (m,)``.
lb, ub : array_like
Lower and upper bounds on the constraint. Each array must have the
shape (m,) or be a scalar, in the latter case a bound will be the same
for all components of the constraint. Use ``np.inf`` with an
appropriate sign to specify a one-sided constraint.
Set components of `lb` and `ub` equal to represent an equality
constraint. Note that you can mix constraints of different types:
interval, one-sided or equality, by setting different components of
`lb` and `ub` as necessary.
jac : {callable, '2-point', '3-point', 'cs'}, optional
Method of computing the Jacobian matrix (an m-by-n matrix,
where element (i, j) is the partial derivative of f[i] with
respect to x[j]). The keywords {'2-point', '3-point',
'cs'} select a finite difference scheme for the numerical estimation.
A callable must have the following signature:
``jac(x) -> {ndarray, sparse matrix}, shape (m, n)``.
Default is '2-point'.
hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy, None}, optional
Method for computing the Hessian matrix. The keywords
{'2-point', '3-point', 'cs'} select a finite difference scheme for
numerical estimation. Alternatively, objects implementing
`HessianUpdateStrategy` interface can be used to approximate the
Hessian. Currently available implementations are:
- `BFGS` (default option)
- `SR1`
A callable must return the Hessian matrix of ``dot(fun, v)`` and
must have the following signature:
``hess(x, v) -> {LinearOperator, sparse matrix, array_like}, shape (n, n)``.
Here ``v`` is ndarray with shape (m,) containing Lagrange multipliers.
keep_feasible : array_like of bool, optional
Whether to keep the constraint components feasible throughout
iterations. A single value set this property for all components.
Default is False. Has no effect for equality constraints.
finite_diff_rel_step: None or array_like, optional
Relative step size for the finite difference approximation. Default is
None, which will select a reasonable value automatically depending
on a finite difference scheme.
finite_diff_jac_sparsity: {None, array_like, sparse matrix}, optional
Defines the sparsity structure of the Jacobian matrix for finite
difference estimation, its shape must be (m, n). If the Jacobian has
only few non-zero elements in *each* row, providing the sparsity
structure will greatly speed up the computations. A zero entry means
that a corresponding element in the Jacobian is identically zero.
If provided, forces the use of 'lsmr' trust-region solver.
If None (default) then dense differencing will be used.
Notes
-----
Finite difference schemes {'2-point', '3-point', 'cs'} may be used for
approximating either the Jacobian or the Hessian. We, however, do not allow
its use for approximating both simultaneously. Hence whenever the Jacobian
is estimated via finite-differences, we require the Hessian to be estimated
using one of the quasi-Newton strategies.
The scheme 'cs' is potentially the most accurate, but requires the function
to correctly handles complex inputs and be analytically continuable to the
complex plane. The scheme '3-point' is more accurate than '2-point' but
requires twice as many operations.
"""
def __init__(self, fun, lb, ub, jac='2-point', hess=BFGS(),
keep_feasible=False, finite_diff_rel_step=None,
finite_diff_jac_sparsity=None):
self.fun = fun
self.lb = lb
self.ub = ub
self.finite_diff_rel_step = finite_diff_rel_step
self.finite_diff_jac_sparsity = finite_diff_jac_sparsity
self.jac = jac
self.hess = hess
self.keep_feasible = keep_feasible
class LinearConstraint(object):
"""Linear constraint on the variables.
The constraint has the general inequality form::
lb <= A.dot(x) <= ub
Here the vector of independent variables x is passed as ndarray of shape
(n,) and the matrix A has shape (m, n).
It is possible to use equal bounds to represent an equality constraint or
infinite bounds to represent a one-sided constraint.
Parameters
----------
A : {array_like, sparse matrix}, shape (m, n)
Matrix defining the constraint.
lb, ub : array_like
Lower and upper bounds on the constraint. Each array must have the
shape (m,) or be a scalar, in the latter case a bound will be the same
for all components of the constraint. Use ``np.inf`` with an
appropriate sign to specify a one-sided constraint.
Set components of `lb` and `ub` equal to represent an equality
constraint. Note that you can mix constraints of different types:
interval, one-sided or equality, by setting different components of
`lb` and `ub` as necessary.
keep_feasible : array_like of bool, optional
Whether to keep the constraint components feasible throughout
iterations. A single value set this property for all components.
Default is False. Has no effect for equality constraints.
"""
def __init__(self, A, lb, ub, keep_feasible=False):
self.A = A
self.lb = lb
self.ub = ub
self.keep_feasible = keep_feasible
class Bounds(object):
"""Bounds constraint on the variables.
The constraint has the general inequality form::
lb <= x <= ub
It is possible to use equal bounds to represent an equality constraint or
infinite bounds to represent a one-sided constraint.
Parameters
----------
lb, ub : array_like, optional
Lower and upper bounds on independent variables. Each array must
have the same size as x or be a scalar, in which case a bound will be
the same for all the variables. Set components of `lb` and `ub` equal
to fix a variable. Use ``np.inf`` with an appropriate sign to disable
bounds on all or some variables. Note that you can mix constraints of
different types: interval, one-sided or equality, by setting different
components of `lb` and `ub` as necessary.
keep_feasible : array_like of bool, optional
Whether to keep the constraint components feasible throughout
iterations. A single value set this property for all components.
Default is False. Has no effect for equality constraints.
"""
def __init__(self, lb, ub, keep_feasible=False):
self.lb = lb
self.ub = ub
self.keep_feasible = keep_feasible
class PreparedConstraint(object):
"""Constraint prepared from a user defined constraint.
On creation it will check whether a constraint definition is valid and
the initial point is feasible. If created successfully, it will contain
the attributes listed below.
Parameters
----------
constraint : {NonlinearConstraint, LinearConstraint`, Bounds}
Constraint to check and prepare.
x0 : array_like
Initial vector of independent variables.
sparse_jacobian : bool or None, optional
If bool, then the Jacobian of the constraint will be converted
to the corresponded format if necessary. If None (default), such
conversion is not made.
finite_diff_bounds : 2-tuple, optional
Lower and upper bounds on the independent variables for the finite
difference approximation, if applicable. Defaults to no bounds.
Attributes
----------
fun : {VectorFunction, LinearVectorFunction, IdentityVectorFunction}
Function defining the constraint wrapped by one of the convenience
classes.
bounds : 2-tuple
Contains lower and upper bounds for the constraints --- lb and ub.
These are converted to ndarray and have a size equal to the number of
the constraints.
keep_feasible : ndarray
Array indicating which components must be kept feasible with a size
equal to the number of the constraints.
"""
def __init__(self, constraint, x0, sparse_jacobian=None,
finite_diff_bounds=(-np.inf, np.inf)):
if isinstance(constraint, NonlinearConstraint):
fun = VectorFunction(constraint.fun, x0,
constraint.jac, constraint.hess,
constraint.finite_diff_rel_step,
constraint.finite_diff_jac_sparsity,
finite_diff_bounds, sparse_jacobian)
elif isinstance(constraint, LinearConstraint):
fun = LinearVectorFunction(constraint.A, x0, sparse_jacobian)
elif isinstance(constraint, Bounds):
fun = IdentityVectorFunction(x0, sparse_jacobian)
else:
raise ValueError("`constraint` of an unknown type is passed.")
m = fun.m
lb = np.asarray(constraint.lb, dtype=float)
ub = np.asarray(constraint.ub, dtype=float)
if lb.ndim == 0:
lb = np.resize(lb, m)
if ub.ndim == 0:
ub = np.resize(ub, m)
keep_feasible = np.asarray(constraint.keep_feasible, dtype=bool)
if keep_feasible.ndim == 0:
keep_feasible = np.resize(keep_feasible, m)
if keep_feasible.shape != (m,):
raise ValueError("`keep_feasible` has a wrong shape.")
mask = keep_feasible & (lb != ub)
f0 = fun.f
if np.any(f0[mask] < lb[mask]) or np.any(f0[mask] > ub[mask]):
raise ValueError("`x0` is infeasible with respect to some "
"inequality constraint with `keep_feasible` "
"set to True.")
self.fun = fun
self.bounds = (lb, ub)
self.keep_feasible = keep_feasible
def new_bounds_to_old(lb, ub, n):
"""Convert the new bounds representation to the old one.
The new representation is a tuple (lb, ub) and the old one is a list
containing n tuples, i-th containing lower and upper bound on a i-th
variable.
"""
lb = np.asarray(lb)
ub = np.asarray(ub)
if lb.ndim == 0:
lb = np.resize(lb, n)
if ub.ndim == 0:
ub = np.resize(ub, n)
lb = [x if x > -np.inf else None for x in lb]
ub = [x if x < np.inf else None for x in ub]
return list(zip(lb, ub))
def old_bound_to_new(bounds):
"""Convert the old bounds representation to the new one.
The new representation is a tuple (lb, ub) and the old one is a list
containing n tuples, i-th containing lower and upper bound on a i-th
variable.
"""
lb, ub = zip(*bounds)
lb = np.array([x if x is not None else -np.inf for x in lb])
ub = np.array([x if x is not None else np.inf for x in ub])
return lb, ub
def strict_bounds(lb, ub, keep_feasible, n_vars):
"""Remove bounds which are not asked to be kept feasible."""
strict_lb = np.resize(lb, n_vars).astype(float)
strict_ub = np.resize(ub, n_vars).astype(float)
keep_feasible = np.resize(keep_feasible, n_vars)
strict_lb[~keep_feasible] = -np.inf
strict_ub[~keep_feasible] = np.inf
return strict_lb, strict_ub
| 12,264 | 41.884615 | 88 |
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|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/nnls.py
|
from __future__ import division, print_function, absolute_import
from . import _nnls
from numpy import asarray_chkfinite, zeros, double
__all__ = ['nnls']
def nnls(A, b, maxiter=None):
"""
Solve ``argmin_x || Ax - b ||_2`` for ``x>=0``. This is a wrapper
for a FORTRAN non-negative least squares solver.
Parameters
----------
A : ndarray
Matrix ``A`` as shown above.
b : ndarray
Right-hand side vector.
maxiter: int, optional
Maximum number of iterations, optional.
Default is ``3 * A.shape[1]``.
Returns
-------
x : ndarray
Solution vector.
rnorm : float
The residual, ``|| Ax-b ||_2``.
Notes
-----
The FORTRAN code was published in the book below. The algorithm
is an active set method. It solves the KKT (Karush-Kuhn-Tucker)
conditions for the non-negative least squares problem.
References
----------
Lawson C., Hanson R.J., (1987) Solving Least Squares Problems, SIAM
"""
A, b = map(asarray_chkfinite, (A, b))
if len(A.shape) != 2:
raise ValueError("expected matrix")
if len(b.shape) != 1:
raise ValueError("expected vector")
m, n = A.shape
if m != b.shape[0]:
raise ValueError("incompatible dimensions")
maxiter = -1 if maxiter is None else int(maxiter)
w = zeros((n,), dtype=double)
zz = zeros((m,), dtype=double)
index = zeros((n,), dtype=int)
x, rnorm, mode = _nnls.nnls(A, m, n, b, w, zz, index, maxiter)
if mode != 1:
raise RuntimeError("too many iterations")
return x, rnorm
| 1,616 | 23.5 | 71 |
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|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/cobyla.py
|
"""
Interface to Constrained Optimization By Linear Approximation
Functions
---------
.. autosummary::
:toctree: generated/
fmin_cobyla
"""
from __future__ import division, print_function, absolute_import
import numpy as np
from scipy._lib.six import callable
from scipy.optimize import _cobyla
from .optimize import OptimizeResult, _check_unknown_options
try:
from itertools import izip
except ImportError:
izip = zip
__all__ = ['fmin_cobyla']
def fmin_cobyla(func, x0, cons, args=(), consargs=None, rhobeg=1.0,
rhoend=1e-4, maxfun=1000, disp=None, catol=2e-4):
"""
Minimize a function using the Constrained Optimization BY Linear
Approximation (COBYLA) method. This method wraps a FORTRAN
implementation of the algorithm.
Parameters
----------
func : callable
Function to minimize. In the form func(x, \\*args).
x0 : ndarray
Initial guess.
cons : sequence
Constraint functions; must all be ``>=0`` (a single function
if only 1 constraint). Each function takes the parameters `x`
as its first argument, and it can return either a single number or
an array or list of numbers.
args : tuple, optional
Extra arguments to pass to function.
consargs : tuple, optional
Extra arguments to pass to constraint functions (default of None means
use same extra arguments as those passed to func).
Use ``()`` for no extra arguments.
rhobeg : float, optional
Reasonable initial changes to the variables.
rhoend : float, optional
Final accuracy in the optimization (not precisely guaranteed). This
is a lower bound on the size of the trust region.
disp : {0, 1, 2, 3}, optional
Controls the frequency of output; 0 implies no output.
maxfun : int, optional
Maximum number of function evaluations.
catol : float, optional
Absolute tolerance for constraint violations.
Returns
-------
x : ndarray
The argument that minimises `f`.
See also
--------
minimize: Interface to minimization algorithms for multivariate
functions. See the 'COBYLA' `method` in particular.
Notes
-----
This algorithm is based on linear approximations to the objective
function and each constraint. We briefly describe the algorithm.
Suppose the function is being minimized over k variables. At the
jth iteration the algorithm has k+1 points v_1, ..., v_(k+1),
an approximate solution x_j, and a radius RHO_j.
(i.e. linear plus a constant) approximations to the objective
function and constraint functions such that their function values
agree with the linear approximation on the k+1 points v_1,.., v_(k+1).
This gives a linear program to solve (where the linear approximations
of the constraint functions are constrained to be non-negative).
However the linear approximations are likely only good
approximations near the current simplex, so the linear program is
given the further requirement that the solution, which
will become x_(j+1), must be within RHO_j from x_j. RHO_j only
decreases, never increases. The initial RHO_j is rhobeg and the
final RHO_j is rhoend. In this way COBYLA's iterations behave
like a trust region algorithm.
Additionally, the linear program may be inconsistent, or the
approximation may give poor improvement. For details about
how these issues are resolved, as well as how the points v_i are
updated, refer to the source code or the references below.
References
----------
Powell M.J.D. (1994), "A direct search optimization method that models
the objective and constraint functions by linear interpolation.", in
Advances in Optimization and Numerical Analysis, eds. S. Gomez and
J-P Hennart, Kluwer Academic (Dordrecht), pp. 51-67
Powell M.J.D. (1998), "Direct search algorithms for optimization
calculations", Acta Numerica 7, 287-336
Powell M.J.D. (2007), "A view of algorithms for optimization without
derivatives", Cambridge University Technical Report DAMTP 2007/NA03
Examples
--------
Minimize the objective function f(x,y) = x*y subject
to the constraints x**2 + y**2 < 1 and y > 0::
>>> def objective(x):
... return x[0]*x[1]
...
>>> def constr1(x):
... return 1 - (x[0]**2 + x[1]**2)
...
>>> def constr2(x):
... return x[1]
...
>>> from scipy.optimize import fmin_cobyla
>>> fmin_cobyla(objective, [0.0, 0.1], [constr1, constr2], rhoend=1e-7)
array([-0.70710685, 0.70710671])
The exact solution is (-sqrt(2)/2, sqrt(2)/2).
"""
err = "cons must be a sequence of callable functions or a single"\
" callable function."
try:
len(cons)
except TypeError:
if callable(cons):
cons = [cons]
else:
raise TypeError(err)
else:
for thisfunc in cons:
if not callable(thisfunc):
raise TypeError(err)
if consargs is None:
consargs = args
# build constraints
con = tuple({'type': 'ineq', 'fun': c, 'args': consargs} for c in cons)
# options
opts = {'rhobeg': rhobeg,
'tol': rhoend,
'disp': disp,
'maxiter': maxfun,
'catol': catol}
sol = _minimize_cobyla(func, x0, args, constraints=con,
**opts)
if disp and not sol['success']:
print("COBYLA failed to find a solution: %s" % (sol.message,))
return sol['x']
def _minimize_cobyla(fun, x0, args=(), constraints=(),
rhobeg=1.0, tol=1e-4, maxiter=1000,
disp=False, catol=2e-4, **unknown_options):
"""
Minimize a scalar function of one or more variables using the
Constrained Optimization BY Linear Approximation (COBYLA) algorithm.
Options
-------
rhobeg : float
Reasonable initial changes to the variables.
tol : float
Final accuracy in the optimization (not precisely guaranteed).
This is a lower bound on the size of the trust region.
disp : bool
Set to True to print convergence messages. If False,
`verbosity` is ignored as set to 0.
maxiter : int
Maximum number of function evaluations.
catol : float
Tolerance (absolute) for constraint violations
"""
_check_unknown_options(unknown_options)
maxfun = maxiter
rhoend = tol
iprint = int(bool(disp))
# check constraints
if isinstance(constraints, dict):
constraints = (constraints, )
for ic, con in enumerate(constraints):
# check type
try:
ctype = con['type'].lower()
except KeyError:
raise KeyError('Constraint %d has no type defined.' % ic)
except TypeError:
raise TypeError('Constraints must be defined using a '
'dictionary.')
except AttributeError:
raise TypeError("Constraint's type must be a string.")
else:
if ctype != 'ineq':
raise ValueError("Constraints of type '%s' not handled by "
"COBYLA." % con['type'])
# check function
if 'fun' not in con:
raise KeyError('Constraint %d has no function defined.' % ic)
# check extra arguments
if 'args' not in con:
con['args'] = ()
# m is the total number of constraint values
# it takes into account that some constraints may be vector-valued
cons_lengths = []
for c in constraints:
f = c['fun'](x0, *c['args'])
try:
cons_length = len(f)
except TypeError:
cons_length = 1
cons_lengths.append(cons_length)
m = sum(cons_lengths)
def calcfc(x, con):
f = fun(x, *args)
i = 0
for size, c in izip(cons_lengths, constraints):
con[i: i + size] = c['fun'](x, *c['args'])
i += size
return f
info = np.zeros(4, np.float64)
xopt, info = _cobyla.minimize(calcfc, m=m, x=np.copy(x0), rhobeg=rhobeg,
rhoend=rhoend, iprint=iprint, maxfun=maxfun,
dinfo=info)
if info[3] > catol:
# Check constraint violation
info[0] = 4
return OptimizeResult(x=xopt,
status=int(info[0]),
success=info[0] == 1,
message={1: 'Optimization terminated successfully.',
2: 'Maximum number of function evaluations '
'has been exceeded.',
3: 'Rounding errors are becoming damaging '
'in COBYLA subroutine.',
4: 'Did not converge to a solution '
'satisfying the constraints. See '
'`maxcv` for magnitude of violation.'
}.get(info[0], 'Unknown exit status.'),
nfev=int(info[1]),
fun=info[2],
maxcv=info[3])
| 9,402 | 33.443223 | 79 |
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|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/nonlin.py
|
r"""
Nonlinear solvers
-----------------
.. currentmodule:: scipy.optimize
This is a collection of general-purpose nonlinear multidimensional
solvers. These solvers find *x* for which *F(x) = 0*. Both *x*
and *F* can be multidimensional.
Routines
~~~~~~~~
Large-scale nonlinear solvers:
.. autosummary::
newton_krylov
anderson
General nonlinear solvers:
.. autosummary::
broyden1
broyden2
Simple iterations:
.. autosummary::
excitingmixing
linearmixing
diagbroyden
Examples
~~~~~~~~
**Small problem**
>>> def F(x):
... return np.cos(x) + x[::-1] - [1, 2, 3, 4]
>>> import scipy.optimize
>>> x = scipy.optimize.broyden1(F, [1,1,1,1], f_tol=1e-14)
>>> x
array([ 4.04674914, 3.91158389, 2.71791677, 1.61756251])
>>> np.cos(x) + x[::-1]
array([ 1., 2., 3., 4.])
**Large problem**
Suppose that we needed to solve the following integrodifferential
equation on the square :math:`[0,1]\times[0,1]`:
.. math::
\nabla^2 P = 10 \left(\int_0^1\int_0^1\cosh(P)\,dx\,dy\right)^2
with :math:`P(x,1) = 1` and :math:`P=0` elsewhere on the boundary of
the square.
The solution can be found using the `newton_krylov` solver:
.. plot::
import numpy as np
from scipy.optimize import newton_krylov
from numpy import cosh, zeros_like, mgrid, zeros
# parameters
nx, ny = 75, 75
hx, hy = 1./(nx-1), 1./(ny-1)
P_left, P_right = 0, 0
P_top, P_bottom = 1, 0
def residual(P):
d2x = zeros_like(P)
d2y = zeros_like(P)
d2x[1:-1] = (P[2:] - 2*P[1:-1] + P[:-2]) / hx/hx
d2x[0] = (P[1] - 2*P[0] + P_left)/hx/hx
d2x[-1] = (P_right - 2*P[-1] + P[-2])/hx/hx
d2y[:,1:-1] = (P[:,2:] - 2*P[:,1:-1] + P[:,:-2])/hy/hy
d2y[:,0] = (P[:,1] - 2*P[:,0] + P_bottom)/hy/hy
d2y[:,-1] = (P_top - 2*P[:,-1] + P[:,-2])/hy/hy
return d2x + d2y - 10*cosh(P).mean()**2
# solve
guess = zeros((nx, ny), float)
sol = newton_krylov(residual, guess, method='lgmres', verbose=1)
print('Residual: %g' % abs(residual(sol)).max())
# visualize
import matplotlib.pyplot as plt
x, y = mgrid[0:1:(nx*1j), 0:1:(ny*1j)]
plt.pcolor(x, y, sol)
plt.colorbar()
plt.show()
"""
# Copyright (C) 2009, Pauli Virtanen <pav@iki.fi>
# Distributed under the same license as Scipy.
from __future__ import division, print_function, absolute_import
import sys
import numpy as np
from scipy._lib.six import callable, exec_, xrange
from scipy.linalg import norm, solve, inv, qr, svd, LinAlgError
from numpy import asarray, dot, vdot
import scipy.sparse.linalg
import scipy.sparse
from scipy.linalg import get_blas_funcs
import inspect
from scipy._lib._util import getargspec_no_self as _getargspec
from .linesearch import scalar_search_wolfe1, scalar_search_armijo
__all__ = [
'broyden1', 'broyden2', 'anderson', 'linearmixing',
'diagbroyden', 'excitingmixing', 'newton_krylov']
#------------------------------------------------------------------------------
# Utility functions
#------------------------------------------------------------------------------
class NoConvergence(Exception):
pass
def maxnorm(x):
return np.absolute(x).max()
def _as_inexact(x):
"""Return `x` as an array, of either floats or complex floats"""
x = asarray(x)
if not np.issubdtype(x.dtype, np.inexact):
return asarray(x, dtype=np.float_)
return x
def _array_like(x, x0):
"""Return ndarray `x` as same array subclass and shape as `x0`"""
x = np.reshape(x, np.shape(x0))
wrap = getattr(x0, '__array_wrap__', x.__array_wrap__)
return wrap(x)
def _safe_norm(v):
if not np.isfinite(v).all():
return np.array(np.inf)
return norm(v)
#------------------------------------------------------------------------------
# Generic nonlinear solver machinery
#------------------------------------------------------------------------------
_doc_parts = dict(
params_basic="""
F : function(x) -> f
Function whose root to find; should take and return an array-like
object.
xin : array_like
Initial guess for the solution
""".strip(),
params_extra="""
iter : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
verbose : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, `NoConvergence` is raised.
f_tol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
f_rtol : float, optional
Relative tolerance for the residual. If omitted, not used.
x_tol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
x_rtol : float, optional
Relative minimum step size. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in the
direction given by the Jacobian approximation. Defaults to 'armijo'.
callback : function, optional
Optional callback function. It is called on every iteration as
``callback(x, f)`` where `x` is the current solution and `f`
the corresponding residual.
Returns
-------
sol : ndarray
An array (of similar array type as `x0`) containing the final solution.
Raises
------
NoConvergence
When a solution was not found.
""".strip()
)
def _set_doc(obj):
if obj.__doc__:
obj.__doc__ = obj.__doc__ % _doc_parts
def nonlin_solve(F, x0, jacobian='krylov', iter=None, verbose=False,
maxiter=None, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None,
tol_norm=None, line_search='armijo', callback=None,
full_output=False, raise_exception=True):
"""
Find a root of a function, in a way suitable for large-scale problems.
Parameters
----------
%(params_basic)s
jacobian : Jacobian
A Jacobian approximation: `Jacobian` object or something that
`asjacobian` can transform to one. Alternatively, a string specifying
which of the builtin Jacobian approximations to use:
krylov, broyden1, broyden2, anderson
diagbroyden, linearmixing, excitingmixing
%(params_extra)s
full_output : bool
If true, returns a dictionary `info` containing convergence
information.
raise_exception : bool
If True, a `NoConvergence` exception is raise if no solution is found.
See Also
--------
asjacobian, Jacobian
Notes
-----
This algorithm implements the inexact Newton method, with
backtracking or full line searches. Several Jacobian
approximations are available, including Krylov and Quasi-Newton
methods.
References
----------
.. [KIM] C. T. Kelley, \"Iterative Methods for Linear and Nonlinear
Equations\". Society for Industrial and Applied Mathematics. (1995)
http://www.siam.org/books/kelley/fr16/index.php
"""
condition = TerminationCondition(f_tol=f_tol, f_rtol=f_rtol,
x_tol=x_tol, x_rtol=x_rtol,
iter=iter, norm=tol_norm)
x0 = _as_inexact(x0)
func = lambda z: _as_inexact(F(_array_like(z, x0))).flatten()
x = x0.flatten()
dx = np.inf
Fx = func(x)
Fx_norm = norm(Fx)
jacobian = asjacobian(jacobian)
jacobian.setup(x.copy(), Fx, func)
if maxiter is None:
if iter is not None:
maxiter = iter + 1
else:
maxiter = 100*(x.size+1)
if line_search is True:
line_search = 'armijo'
elif line_search is False:
line_search = None
if line_search not in (None, 'armijo', 'wolfe'):
raise ValueError("Invalid line search")
# Solver tolerance selection
gamma = 0.9
eta_max = 0.9999
eta_treshold = 0.1
eta = 1e-3
for n in xrange(maxiter):
status = condition.check(Fx, x, dx)
if status:
break
# The tolerance, as computed for scipy.sparse.linalg.* routines
tol = min(eta, eta*Fx_norm)
dx = -jacobian.solve(Fx, tol=tol)
if norm(dx) == 0:
raise ValueError("Jacobian inversion yielded zero vector. "
"This indicates a bug in the Jacobian "
"approximation.")
# Line search, or Newton step
if line_search:
s, x, Fx, Fx_norm_new = _nonlin_line_search(func, x, Fx, dx,
line_search)
else:
s = 1.0
x = x + dx
Fx = func(x)
Fx_norm_new = norm(Fx)
jacobian.update(x.copy(), Fx)
if callback:
callback(x, Fx)
# Adjust forcing parameters for inexact methods
eta_A = gamma * Fx_norm_new**2 / Fx_norm**2
if gamma * eta**2 < eta_treshold:
eta = min(eta_max, eta_A)
else:
eta = min(eta_max, max(eta_A, gamma*eta**2))
Fx_norm = Fx_norm_new
# Print status
if verbose:
sys.stdout.write("%d: |F(x)| = %g; step %g; tol %g\n" % (
n, norm(Fx), s, eta))
sys.stdout.flush()
else:
if raise_exception:
raise NoConvergence(_array_like(x, x0))
else:
status = 2
if full_output:
info = {'nit': condition.iteration,
'fun': Fx,
'status': status,
'success': status == 1,
'message': {1: 'A solution was found at the specified '
'tolerance.',
2: 'The maximum number of iterations allowed '
'has been reached.'
}[status]
}
return _array_like(x, x0), info
else:
return _array_like(x, x0)
_set_doc(nonlin_solve)
def _nonlin_line_search(func, x, Fx, dx, search_type='armijo', rdiff=1e-8,
smin=1e-2):
tmp_s = [0]
tmp_Fx = [Fx]
tmp_phi = [norm(Fx)**2]
s_norm = norm(x) / norm(dx)
def phi(s, store=True):
if s == tmp_s[0]:
return tmp_phi[0]
xt = x + s*dx
v = func(xt)
p = _safe_norm(v)**2
if store:
tmp_s[0] = s
tmp_phi[0] = p
tmp_Fx[0] = v
return p
def derphi(s):
ds = (abs(s) + s_norm + 1) * rdiff
return (phi(s+ds, store=False) - phi(s)) / ds
if search_type == 'wolfe':
s, phi1, phi0 = scalar_search_wolfe1(phi, derphi, tmp_phi[0],
xtol=1e-2, amin=smin)
elif search_type == 'armijo':
s, phi1 = scalar_search_armijo(phi, tmp_phi[0], -tmp_phi[0],
amin=smin)
if s is None:
# XXX: No suitable step length found. Take the full Newton step,
# and hope for the best.
s = 1.0
x = x + s*dx
if s == tmp_s[0]:
Fx = tmp_Fx[0]
else:
Fx = func(x)
Fx_norm = norm(Fx)
return s, x, Fx, Fx_norm
class TerminationCondition(object):
"""
Termination condition for an iteration. It is terminated if
- |F| < f_rtol*|F_0|, AND
- |F| < f_tol
AND
- |dx| < x_rtol*|x|, AND
- |dx| < x_tol
"""
def __init__(self, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None,
iter=None, norm=maxnorm):
if f_tol is None:
f_tol = np.finfo(np.float_).eps ** (1./3)
if f_rtol is None:
f_rtol = np.inf
if x_tol is None:
x_tol = np.inf
if x_rtol is None:
x_rtol = np.inf
self.x_tol = x_tol
self.x_rtol = x_rtol
self.f_tol = f_tol
self.f_rtol = f_rtol
if norm is None:
self.norm = maxnorm
else:
self.norm = norm
self.iter = iter
self.f0_norm = None
self.iteration = 0
def check(self, f, x, dx):
self.iteration += 1
f_norm = self.norm(f)
x_norm = self.norm(x)
dx_norm = self.norm(dx)
if self.f0_norm is None:
self.f0_norm = f_norm
if f_norm == 0:
return 1
if self.iter is not None:
# backwards compatibility with Scipy 0.6.0
return 2 * (self.iteration > self.iter)
# NB: condition must succeed for rtol=inf even if norm == 0
return int((f_norm <= self.f_tol
and f_norm/self.f_rtol <= self.f0_norm)
and (dx_norm <= self.x_tol
and dx_norm/self.x_rtol <= x_norm))
#------------------------------------------------------------------------------
# Generic Jacobian approximation
#------------------------------------------------------------------------------
class Jacobian(object):
"""
Common interface for Jacobians or Jacobian approximations.
The optional methods come useful when implementing trust region
etc. algorithms that often require evaluating transposes of the
Jacobian.
Methods
-------
solve
Returns J^-1 * v
update
Updates Jacobian to point `x` (where the function has residual `Fx`)
matvec : optional
Returns J * v
rmatvec : optional
Returns A^H * v
rsolve : optional
Returns A^-H * v
matmat : optional
Returns A * V, where V is a dense matrix with dimensions (N,K).
todense : optional
Form the dense Jacobian matrix. Necessary for dense trust region
algorithms, and useful for testing.
Attributes
----------
shape
Matrix dimensions (M, N)
dtype
Data type of the matrix.
func : callable, optional
Function the Jacobian corresponds to
"""
def __init__(self, **kw):
names = ["solve", "update", "matvec", "rmatvec", "rsolve",
"matmat", "todense", "shape", "dtype"]
for name, value in kw.items():
if name not in names:
raise ValueError("Unknown keyword argument %s" % name)
if value is not None:
setattr(self, name, kw[name])
if hasattr(self, 'todense'):
self.__array__ = lambda: self.todense()
def aspreconditioner(self):
return InverseJacobian(self)
def solve(self, v, tol=0):
raise NotImplementedError
def update(self, x, F):
pass
def setup(self, x, F, func):
self.func = func
self.shape = (F.size, x.size)
self.dtype = F.dtype
if self.__class__.setup is Jacobian.setup:
# Call on the first point unless overridden
self.update(x, F)
class InverseJacobian(object):
def __init__(self, jacobian):
self.jacobian = jacobian
self.matvec = jacobian.solve
self.update = jacobian.update
if hasattr(jacobian, 'setup'):
self.setup = jacobian.setup
if hasattr(jacobian, 'rsolve'):
self.rmatvec = jacobian.rsolve
@property
def shape(self):
return self.jacobian.shape
@property
def dtype(self):
return self.jacobian.dtype
def asjacobian(J):
"""
Convert given object to one suitable for use as a Jacobian.
"""
spsolve = scipy.sparse.linalg.spsolve
if isinstance(J, Jacobian):
return J
elif inspect.isclass(J) and issubclass(J, Jacobian):
return J()
elif isinstance(J, np.ndarray):
if J.ndim > 2:
raise ValueError('array must have rank <= 2')
J = np.atleast_2d(np.asarray(J))
if J.shape[0] != J.shape[1]:
raise ValueError('array must be square')
return Jacobian(matvec=lambda v: dot(J, v),
rmatvec=lambda v: dot(J.conj().T, v),
solve=lambda v: solve(J, v),
rsolve=lambda v: solve(J.conj().T, v),
dtype=J.dtype, shape=J.shape)
elif scipy.sparse.isspmatrix(J):
if J.shape[0] != J.shape[1]:
raise ValueError('matrix must be square')
return Jacobian(matvec=lambda v: J*v,
rmatvec=lambda v: J.conj().T * v,
solve=lambda v: spsolve(J, v),
rsolve=lambda v: spsolve(J.conj().T, v),
dtype=J.dtype, shape=J.shape)
elif hasattr(J, 'shape') and hasattr(J, 'dtype') and hasattr(J, 'solve'):
return Jacobian(matvec=getattr(J, 'matvec'),
rmatvec=getattr(J, 'rmatvec'),
solve=J.solve,
rsolve=getattr(J, 'rsolve'),
update=getattr(J, 'update'),
setup=getattr(J, 'setup'),
dtype=J.dtype,
shape=J.shape)
elif callable(J):
# Assume it's a function J(x) that returns the Jacobian
class Jac(Jacobian):
def update(self, x, F):
self.x = x
def solve(self, v, tol=0):
m = J(self.x)
if isinstance(m, np.ndarray):
return solve(m, v)
elif scipy.sparse.isspmatrix(m):
return spsolve(m, v)
else:
raise ValueError("Unknown matrix type")
def matvec(self, v):
m = J(self.x)
if isinstance(m, np.ndarray):
return dot(m, v)
elif scipy.sparse.isspmatrix(m):
return m*v
else:
raise ValueError("Unknown matrix type")
def rsolve(self, v, tol=0):
m = J(self.x)
if isinstance(m, np.ndarray):
return solve(m.conj().T, v)
elif scipy.sparse.isspmatrix(m):
return spsolve(m.conj().T, v)
else:
raise ValueError("Unknown matrix type")
def rmatvec(self, v):
m = J(self.x)
if isinstance(m, np.ndarray):
return dot(m.conj().T, v)
elif scipy.sparse.isspmatrix(m):
return m.conj().T * v
else:
raise ValueError("Unknown matrix type")
return Jac()
elif isinstance(J, str):
return dict(broyden1=BroydenFirst,
broyden2=BroydenSecond,
anderson=Anderson,
diagbroyden=DiagBroyden,
linearmixing=LinearMixing,
excitingmixing=ExcitingMixing,
krylov=KrylovJacobian)[J]()
else:
raise TypeError('Cannot convert object to a Jacobian')
#------------------------------------------------------------------------------
# Broyden
#------------------------------------------------------------------------------
class GenericBroyden(Jacobian):
def setup(self, x0, f0, func):
Jacobian.setup(self, x0, f0, func)
self.last_f = f0
self.last_x = x0
if hasattr(self, 'alpha') and self.alpha is None:
# Autoscale the initial Jacobian parameter
# unless we have already guessed the solution.
normf0 = norm(f0)
if normf0:
self.alpha = 0.5*max(norm(x0), 1) / normf0
else:
self.alpha = 1.0
def _update(self, x, f, dx, df, dx_norm, df_norm):
raise NotImplementedError
def update(self, x, f):
df = f - self.last_f
dx = x - self.last_x
self._update(x, f, dx, df, norm(dx), norm(df))
self.last_f = f
self.last_x = x
class LowRankMatrix(object):
r"""
A matrix represented as
.. math:: \alpha I + \sum_{n=0}^{n=M} c_n d_n^\dagger
However, if the rank of the matrix reaches the dimension of the vectors,
full matrix representation will be used thereon.
"""
def __init__(self, alpha, n, dtype):
self.alpha = alpha
self.cs = []
self.ds = []
self.n = n
self.dtype = dtype
self.collapsed = None
@staticmethod
def _matvec(v, alpha, cs, ds):
axpy, scal, dotc = get_blas_funcs(['axpy', 'scal', 'dotc'],
cs[:1] + [v])
w = alpha * v
for c, d in zip(cs, ds):
a = dotc(d, v)
w = axpy(c, w, w.size, a)
return w
@staticmethod
def _solve(v, alpha, cs, ds):
"""Evaluate w = M^-1 v"""
if len(cs) == 0:
return v/alpha
# (B + C D^H)^-1 = B^-1 - B^-1 C (I + D^H B^-1 C)^-1 D^H B^-1
axpy, dotc = get_blas_funcs(['axpy', 'dotc'], cs[:1] + [v])
c0 = cs[0]
A = alpha * np.identity(len(cs), dtype=c0.dtype)
for i, d in enumerate(ds):
for j, c in enumerate(cs):
A[i,j] += dotc(d, c)
q = np.zeros(len(cs), dtype=c0.dtype)
for j, d in enumerate(ds):
q[j] = dotc(d, v)
q /= alpha
q = solve(A, q)
w = v/alpha
for c, qc in zip(cs, q):
w = axpy(c, w, w.size, -qc)
return w
def matvec(self, v):
"""Evaluate w = M v"""
if self.collapsed is not None:
return np.dot(self.collapsed, v)
return LowRankMatrix._matvec(v, self.alpha, self.cs, self.ds)
def rmatvec(self, v):
"""Evaluate w = M^H v"""
if self.collapsed is not None:
return np.dot(self.collapsed.T.conj(), v)
return LowRankMatrix._matvec(v, np.conj(self.alpha), self.ds, self.cs)
def solve(self, v, tol=0):
"""Evaluate w = M^-1 v"""
if self.collapsed is not None:
return solve(self.collapsed, v)
return LowRankMatrix._solve(v, self.alpha, self.cs, self.ds)
def rsolve(self, v, tol=0):
"""Evaluate w = M^-H v"""
if self.collapsed is not None:
return solve(self.collapsed.T.conj(), v)
return LowRankMatrix._solve(v, np.conj(self.alpha), self.ds, self.cs)
def append(self, c, d):
if self.collapsed is not None:
self.collapsed += c[:,None] * d[None,:].conj()
return
self.cs.append(c)
self.ds.append(d)
if len(self.cs) > c.size:
self.collapse()
def __array__(self):
if self.collapsed is not None:
return self.collapsed
Gm = self.alpha*np.identity(self.n, dtype=self.dtype)
for c, d in zip(self.cs, self.ds):
Gm += c[:,None]*d[None,:].conj()
return Gm
def collapse(self):
"""Collapse the low-rank matrix to a full-rank one."""
self.collapsed = np.array(self)
self.cs = None
self.ds = None
self.alpha = None
def restart_reduce(self, rank):
"""
Reduce the rank of the matrix by dropping all vectors.
"""
if self.collapsed is not None:
return
assert rank > 0
if len(self.cs) > rank:
del self.cs[:]
del self.ds[:]
def simple_reduce(self, rank):
"""
Reduce the rank of the matrix by dropping oldest vectors.
"""
if self.collapsed is not None:
return
assert rank > 0
while len(self.cs) > rank:
del self.cs[0]
del self.ds[0]
def svd_reduce(self, max_rank, to_retain=None):
"""
Reduce the rank of the matrix by retaining some SVD components.
This corresponds to the \"Broyden Rank Reduction Inverse\"
algorithm described in [1]_.
Note that the SVD decomposition can be done by solving only a
problem whose size is the effective rank of this matrix, which
is viable even for large problems.
Parameters
----------
max_rank : int
Maximum rank of this matrix after reduction.
to_retain : int, optional
Number of SVD components to retain when reduction is done
(ie. rank > max_rank). Default is ``max_rank - 2``.
References
----------
.. [1] B.A. van der Rotten, PhD thesis,
\"A limited memory Broyden method to solve high-dimensional
systems of nonlinear equations\". Mathematisch Instituut,
Universiteit Leiden, The Netherlands (2003).
http://www.math.leidenuniv.nl/scripties/Rotten.pdf
"""
if self.collapsed is not None:
return
p = max_rank
if to_retain is not None:
q = to_retain
else:
q = p - 2
if self.cs:
p = min(p, len(self.cs[0]))
q = max(0, min(q, p-1))
m = len(self.cs)
if m < p:
# nothing to do
return
C = np.array(self.cs).T
D = np.array(self.ds).T
D, R = qr(D, mode='economic')
C = dot(C, R.T.conj())
U, S, WH = svd(C, full_matrices=False, compute_uv=True)
C = dot(C, inv(WH))
D = dot(D, WH.T.conj())
for k in xrange(q):
self.cs[k] = C[:,k].copy()
self.ds[k] = D[:,k].copy()
del self.cs[q:]
del self.ds[q:]
_doc_parts['broyden_params'] = """
alpha : float, optional
Initial guess for the Jacobian is ``(-1/alpha)``.
reduction_method : str or tuple, optional
Method used in ensuring that the rank of the Broyden matrix
stays low. Can either be a string giving the name of the method,
or a tuple of the form ``(method, param1, param2, ...)``
that gives the name of the method and values for additional parameters.
Methods available:
- ``restart``: drop all matrix columns. Has no extra parameters.
- ``simple``: drop oldest matrix column. Has no extra parameters.
- ``svd``: keep only the most significant SVD components.
Takes an extra parameter, ``to_retain``, which determines the
number of SVD components to retain when rank reduction is done.
Default is ``max_rank - 2``.
max_rank : int, optional
Maximum rank for the Broyden matrix.
Default is infinity (ie., no rank reduction).
""".strip()
class BroydenFirst(GenericBroyden):
r"""
Find a root of a function, using Broyden's first Jacobian approximation.
This method is also known as \"Broyden's good method\".
Parameters
----------
%(params_basic)s
%(broyden_params)s
%(params_extra)s
Notes
-----
This algorithm implements the inverse Jacobian Quasi-Newton update
.. math:: H_+ = H + (dx - H df) dx^\dagger H / ( dx^\dagger H df)
which corresponds to Broyden's first Jacobian update
.. math:: J_+ = J + (df - J dx) dx^\dagger / dx^\dagger dx
References
----------
.. [1] B.A. van der Rotten, PhD thesis,
\"A limited memory Broyden method to solve high-dimensional
systems of nonlinear equations\". Mathematisch Instituut,
Universiteit Leiden, The Netherlands (2003).
http://www.math.leidenuniv.nl/scripties/Rotten.pdf
"""
def __init__(self, alpha=None, reduction_method='restart', max_rank=None):
GenericBroyden.__init__(self)
self.alpha = alpha
self.Gm = None
if max_rank is None:
max_rank = np.inf
self.max_rank = max_rank
if isinstance(reduction_method, str):
reduce_params = ()
else:
reduce_params = reduction_method[1:]
reduction_method = reduction_method[0]
reduce_params = (max_rank - 1,) + reduce_params
if reduction_method == 'svd':
self._reduce = lambda: self.Gm.svd_reduce(*reduce_params)
elif reduction_method == 'simple':
self._reduce = lambda: self.Gm.simple_reduce(*reduce_params)
elif reduction_method == 'restart':
self._reduce = lambda: self.Gm.restart_reduce(*reduce_params)
else:
raise ValueError("Unknown rank reduction method '%s'" %
reduction_method)
def setup(self, x, F, func):
GenericBroyden.setup(self, x, F, func)
self.Gm = LowRankMatrix(-self.alpha, self.shape[0], self.dtype)
def todense(self):
return inv(self.Gm)
def solve(self, f, tol=0):
r = self.Gm.matvec(f)
if not np.isfinite(r).all():
# singular; reset the Jacobian approximation
self.setup(self.last_x, self.last_f, self.func)
return self.Gm.matvec(f)
def matvec(self, f):
return self.Gm.solve(f)
def rsolve(self, f, tol=0):
return self.Gm.rmatvec(f)
def rmatvec(self, f):
return self.Gm.rsolve(f)
def _update(self, x, f, dx, df, dx_norm, df_norm):
self._reduce() # reduce first to preserve secant condition
v = self.Gm.rmatvec(dx)
c = dx - self.Gm.matvec(df)
d = v / vdot(df, v)
self.Gm.append(c, d)
class BroydenSecond(BroydenFirst):
"""
Find a root of a function, using Broyden\'s second Jacobian approximation.
This method is also known as \"Broyden's bad method\".
Parameters
----------
%(params_basic)s
%(broyden_params)s
%(params_extra)s
Notes
-----
This algorithm implements the inverse Jacobian Quasi-Newton update
.. math:: H_+ = H + (dx - H df) df^\\dagger / ( df^\\dagger df)
corresponding to Broyden's second method.
References
----------
.. [1] B.A. van der Rotten, PhD thesis,
\"A limited memory Broyden method to solve high-dimensional
systems of nonlinear equations\". Mathematisch Instituut,
Universiteit Leiden, The Netherlands (2003).
http://www.math.leidenuniv.nl/scripties/Rotten.pdf
"""
def _update(self, x, f, dx, df, dx_norm, df_norm):
self._reduce() # reduce first to preserve secant condition
v = df
c = dx - self.Gm.matvec(df)
d = v / df_norm**2
self.Gm.append(c, d)
#------------------------------------------------------------------------------
# Broyden-like (restricted memory)
#------------------------------------------------------------------------------
class Anderson(GenericBroyden):
"""
Find a root of a function, using (extended) Anderson mixing.
The Jacobian is formed by for a 'best' solution in the space
spanned by last `M` vectors. As a result, only a MxM matrix
inversions and MxN multiplications are required. [Ey]_
Parameters
----------
%(params_basic)s
alpha : float, optional
Initial guess for the Jacobian is (-1/alpha).
M : float, optional
Number of previous vectors to retain. Defaults to 5.
w0 : float, optional
Regularization parameter for numerical stability.
Compared to unity, good values of the order of 0.01.
%(params_extra)s
References
----------
.. [Ey] V. Eyert, J. Comp. Phys., 124, 271 (1996).
"""
# Note:
#
# Anderson method maintains a rank M approximation of the inverse Jacobian,
#
# J^-1 v ~ -v*alpha + (dX + alpha dF) A^-1 dF^H v
# A = W + dF^H dF
# W = w0^2 diag(dF^H dF)
#
# so that for w0 = 0 the secant condition applies for last M iterates, ie.,
#
# J^-1 df_j = dx_j
#
# for all j = 0 ... M-1.
#
# Moreover, (from Sherman-Morrison-Woodbury formula)
#
# J v ~ [ b I - b^2 C (I + b dF^H A^-1 C)^-1 dF^H ] v
# C = (dX + alpha dF) A^-1
# b = -1/alpha
#
# and after simplification
#
# J v ~ -v/alpha + (dX/alpha + dF) (dF^H dX - alpha W)^-1 dF^H v
#
def __init__(self, alpha=None, w0=0.01, M=5):
GenericBroyden.__init__(self)
self.alpha = alpha
self.M = M
self.dx = []
self.df = []
self.gamma = None
self.w0 = w0
def solve(self, f, tol=0):
dx = -self.alpha*f
n = len(self.dx)
if n == 0:
return dx
df_f = np.empty(n, dtype=f.dtype)
for k in xrange(n):
df_f[k] = vdot(self.df[k], f)
try:
gamma = solve(self.a, df_f)
except LinAlgError:
# singular; reset the Jacobian approximation
del self.dx[:]
del self.df[:]
return dx
for m in xrange(n):
dx += gamma[m]*(self.dx[m] + self.alpha*self.df[m])
return dx
def matvec(self, f):
dx = -f/self.alpha
n = len(self.dx)
if n == 0:
return dx
df_f = np.empty(n, dtype=f.dtype)
for k in xrange(n):
df_f[k] = vdot(self.df[k], f)
b = np.empty((n, n), dtype=f.dtype)
for i in xrange(n):
for j in xrange(n):
b[i,j] = vdot(self.df[i], self.dx[j])
if i == j and self.w0 != 0:
b[i,j] -= vdot(self.df[i], self.df[i])*self.w0**2*self.alpha
gamma = solve(b, df_f)
for m in xrange(n):
dx += gamma[m]*(self.df[m] + self.dx[m]/self.alpha)
return dx
def _update(self, x, f, dx, df, dx_norm, df_norm):
if self.M == 0:
return
self.dx.append(dx)
self.df.append(df)
while len(self.dx) > self.M:
self.dx.pop(0)
self.df.pop(0)
n = len(self.dx)
a = np.zeros((n, n), dtype=f.dtype)
for i in xrange(n):
for j in xrange(i, n):
if i == j:
wd = self.w0**2
else:
wd = 0
a[i,j] = (1+wd)*vdot(self.df[i], self.df[j])
a += np.triu(a, 1).T.conj()
self.a = a
#------------------------------------------------------------------------------
# Simple iterations
#------------------------------------------------------------------------------
class DiagBroyden(GenericBroyden):
"""
Find a root of a function, using diagonal Broyden Jacobian approximation.
The Jacobian approximation is derived from previous iterations, by
retaining only the diagonal of Broyden matrices.
.. warning::
This algorithm may be useful for specific problems, but whether
it will work may depend strongly on the problem.
Parameters
----------
%(params_basic)s
alpha : float, optional
Initial guess for the Jacobian is (-1/alpha).
%(params_extra)s
"""
def __init__(self, alpha=None):
GenericBroyden.__init__(self)
self.alpha = alpha
def setup(self, x, F, func):
GenericBroyden.setup(self, x, F, func)
self.d = np.ones((self.shape[0],), dtype=self.dtype) / self.alpha
def solve(self, f, tol=0):
return -f / self.d
def matvec(self, f):
return -f * self.d
def rsolve(self, f, tol=0):
return -f / self.d.conj()
def rmatvec(self, f):
return -f * self.d.conj()
def todense(self):
return np.diag(-self.d)
def _update(self, x, f, dx, df, dx_norm, df_norm):
self.d -= (df + self.d*dx)*dx/dx_norm**2
class LinearMixing(GenericBroyden):
"""
Find a root of a function, using a scalar Jacobian approximation.
.. warning::
This algorithm may be useful for specific problems, but whether
it will work may depend strongly on the problem.
Parameters
----------
%(params_basic)s
alpha : float, optional
The Jacobian approximation is (-1/alpha).
%(params_extra)s
"""
def __init__(self, alpha=None):
GenericBroyden.__init__(self)
self.alpha = alpha
def solve(self, f, tol=0):
return -f*self.alpha
def matvec(self, f):
return -f/self.alpha
def rsolve(self, f, tol=0):
return -f*np.conj(self.alpha)
def rmatvec(self, f):
return -f/np.conj(self.alpha)
def todense(self):
return np.diag(-np.ones(self.shape[0])/self.alpha)
def _update(self, x, f, dx, df, dx_norm, df_norm):
pass
class ExcitingMixing(GenericBroyden):
"""
Find a root of a function, using a tuned diagonal Jacobian approximation.
The Jacobian matrix is diagonal and is tuned on each iteration.
.. warning::
This algorithm may be useful for specific problems, but whether
it will work may depend strongly on the problem.
Parameters
----------
%(params_basic)s
alpha : float, optional
Initial Jacobian approximation is (-1/alpha).
alphamax : float, optional
The entries of the diagonal Jacobian are kept in the range
``[alpha, alphamax]``.
%(params_extra)s
"""
def __init__(self, alpha=None, alphamax=1.0):
GenericBroyden.__init__(self)
self.alpha = alpha
self.alphamax = alphamax
self.beta = None
def setup(self, x, F, func):
GenericBroyden.setup(self, x, F, func)
self.beta = self.alpha * np.ones((self.shape[0],), dtype=self.dtype)
def solve(self, f, tol=0):
return -f*self.beta
def matvec(self, f):
return -f/self.beta
def rsolve(self, f, tol=0):
return -f*self.beta.conj()
def rmatvec(self, f):
return -f/self.beta.conj()
def todense(self):
return np.diag(-1/self.beta)
def _update(self, x, f, dx, df, dx_norm, df_norm):
incr = f*self.last_f > 0
self.beta[incr] += self.alpha
self.beta[~incr] = self.alpha
np.clip(self.beta, 0, self.alphamax, out=self.beta)
#------------------------------------------------------------------------------
# Iterative/Krylov approximated Jacobians
#------------------------------------------------------------------------------
class KrylovJacobian(Jacobian):
r"""
Find a root of a function, using Krylov approximation for inverse Jacobian.
This method is suitable for solving large-scale problems.
Parameters
----------
%(params_basic)s
rdiff : float, optional
Relative step size to use in numerical differentiation.
method : {'lgmres', 'gmres', 'bicgstab', 'cgs', 'minres'} or function
Krylov method to use to approximate the Jacobian.
Can be a string, or a function implementing the same interface as
the iterative solvers in `scipy.sparse.linalg`.
The default is `scipy.sparse.linalg.lgmres`.
inner_M : LinearOperator or InverseJacobian
Preconditioner for the inner Krylov iteration.
Note that you can use also inverse Jacobians as (adaptive)
preconditioners. For example,
>>> from scipy.optimize.nonlin import BroydenFirst, KrylovJacobian
>>> from scipy.optimize.nonlin import InverseJacobian
>>> jac = BroydenFirst()
>>> kjac = KrylovJacobian(inner_M=InverseJacobian(jac))
If the preconditioner has a method named 'update', it will be called
as ``update(x, f)`` after each nonlinear step, with ``x`` giving
the current point, and ``f`` the current function value.
inner_tol, inner_maxiter, ...
Parameters to pass on to the \"inner\" Krylov solver.
See `scipy.sparse.linalg.gmres` for details.
outer_k : int, optional
Size of the subspace kept across LGMRES nonlinear iterations.
See `scipy.sparse.linalg.lgmres` for details.
%(params_extra)s
See Also
--------
scipy.sparse.linalg.gmres
scipy.sparse.linalg.lgmres
Notes
-----
This function implements a Newton-Krylov solver. The basic idea is
to compute the inverse of the Jacobian with an iterative Krylov
method. These methods require only evaluating the Jacobian-vector
products, which are conveniently approximated by a finite difference:
.. math:: J v \approx (f(x + \omega*v/|v|) - f(x)) / \omega
Due to the use of iterative matrix inverses, these methods can
deal with large nonlinear problems.
Scipy's `scipy.sparse.linalg` module offers a selection of Krylov
solvers to choose from. The default here is `lgmres`, which is a
variant of restarted GMRES iteration that reuses some of the
information obtained in the previous Newton steps to invert
Jacobians in subsequent steps.
For a review on Newton-Krylov methods, see for example [1]_,
and for the LGMRES sparse inverse method, see [2]_.
References
----------
.. [1] D.A. Knoll and D.E. Keyes, J. Comp. Phys. 193, 357 (2004).
:doi:`10.1016/j.jcp.2003.08.010`
.. [2] A.H. Baker and E.R. Jessup and T. Manteuffel,
SIAM J. Matrix Anal. Appl. 26, 962 (2005).
:doi:`10.1137/S0895479803422014`
"""
def __init__(self, rdiff=None, method='lgmres', inner_maxiter=20,
inner_M=None, outer_k=10, **kw):
self.preconditioner = inner_M
self.rdiff = rdiff
self.method = dict(
bicgstab=scipy.sparse.linalg.bicgstab,
gmres=scipy.sparse.linalg.gmres,
lgmres=scipy.sparse.linalg.lgmres,
cgs=scipy.sparse.linalg.cgs,
minres=scipy.sparse.linalg.minres,
).get(method, method)
self.method_kw = dict(maxiter=inner_maxiter, M=self.preconditioner)
if self.method is scipy.sparse.linalg.gmres:
# Replace GMRES's outer iteration with Newton steps
self.method_kw['restrt'] = inner_maxiter
self.method_kw['maxiter'] = 1
self.method_kw.setdefault('atol', 0)
elif self.method is scipy.sparse.linalg.gcrotmk:
self.method_kw.setdefault('atol', 0)
elif self.method is scipy.sparse.linalg.lgmres:
self.method_kw['outer_k'] = outer_k
# Replace LGMRES's outer iteration with Newton steps
self.method_kw['maxiter'] = 1
# Carry LGMRES's `outer_v` vectors across nonlinear iterations
self.method_kw.setdefault('outer_v', [])
self.method_kw.setdefault('prepend_outer_v', True)
# But don't carry the corresponding Jacobian*v products, in case
# the Jacobian changes a lot in the nonlinear step
#
# XXX: some trust-region inspired ideas might be more efficient...
# See eg. Brown & Saad. But needs to be implemented separately
# since it's not an inexact Newton method.
self.method_kw.setdefault('store_outer_Av', False)
self.method_kw.setdefault('atol', 0)
for key, value in kw.items():
if not key.startswith('inner_'):
raise ValueError("Unknown parameter %s" % key)
self.method_kw[key[6:]] = value
def _update_diff_step(self):
mx = abs(self.x0).max()
mf = abs(self.f0).max()
self.omega = self.rdiff * max(1, mx) / max(1, mf)
def matvec(self, v):
nv = norm(v)
if nv == 0:
return 0*v
sc = self.omega / nv
r = (self.func(self.x0 + sc*v) - self.f0) / sc
if not np.all(np.isfinite(r)) and np.all(np.isfinite(v)):
raise ValueError('Function returned non-finite results')
return r
def solve(self, rhs, tol=0):
if 'tol' in self.method_kw:
sol, info = self.method(self.op, rhs, **self.method_kw)
else:
sol, info = self.method(self.op, rhs, tol=tol, **self.method_kw)
return sol
def update(self, x, f):
self.x0 = x
self.f0 = f
self._update_diff_step()
# Update also the preconditioner, if possible
if self.preconditioner is not None:
if hasattr(self.preconditioner, 'update'):
self.preconditioner.update(x, f)
def setup(self, x, f, func):
Jacobian.setup(self, x, f, func)
self.x0 = x
self.f0 = f
self.op = scipy.sparse.linalg.aslinearoperator(self)
if self.rdiff is None:
self.rdiff = np.finfo(x.dtype).eps ** (1./2)
self._update_diff_step()
# Setup also the preconditioner, if possible
if self.preconditioner is not None:
if hasattr(self.preconditioner, 'setup'):
self.preconditioner.setup(x, f, func)
#------------------------------------------------------------------------------
# Wrapper functions
#------------------------------------------------------------------------------
def _nonlin_wrapper(name, jac):
"""
Construct a solver wrapper with given name and jacobian approx.
It inspects the keyword arguments of ``jac.__init__``, and allows to
use the same arguments in the wrapper function, in addition to the
keyword arguments of `nonlin_solve`
"""
args, varargs, varkw, defaults = _getargspec(jac.__init__)
kwargs = list(zip(args[-len(defaults):], defaults))
kw_str = ", ".join(["%s=%r" % (k, v) for k, v in kwargs])
if kw_str:
kw_str = ", " + kw_str
kwkw_str = ", ".join(["%s=%s" % (k, k) for k, v in kwargs])
if kwkw_str:
kwkw_str = kwkw_str + ", "
# Construct the wrapper function so that its keyword arguments
# are visible in pydoc.help etc.
wrapper = """
def %(name)s(F, xin, iter=None %(kw)s, verbose=False, maxiter=None,
f_tol=None, f_rtol=None, x_tol=None, x_rtol=None,
tol_norm=None, line_search='armijo', callback=None, **kw):
jac = %(jac)s(%(kwkw)s **kw)
return nonlin_solve(F, xin, jac, iter, verbose, maxiter,
f_tol, f_rtol, x_tol, x_rtol, tol_norm, line_search,
callback)
"""
wrapper = wrapper % dict(name=name, kw=kw_str, jac=jac.__name__,
kwkw=kwkw_str)
ns = {}
ns.update(globals())
exec_(wrapper, ns)
func = ns[name]
func.__doc__ = jac.__doc__
_set_doc(func)
return func
broyden1 = _nonlin_wrapper('broyden1', BroydenFirst)
broyden2 = _nonlin_wrapper('broyden2', BroydenSecond)
anderson = _nonlin_wrapper('anderson', Anderson)
linearmixing = _nonlin_wrapper('linearmixing', LinearMixing)
diagbroyden = _nonlin_wrapper('diagbroyden', DiagBroyden)
excitingmixing = _nonlin_wrapper('excitingmixing', ExcitingMixing)
newton_krylov = _nonlin_wrapper('newton_krylov', KrylovJacobian)
| 46,969 | 29.361991 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_numdiff.py
|
"""Routines for numerical differentiation."""
from __future__ import division
import numpy as np
from numpy.linalg import norm
from scipy.sparse.linalg import LinearOperator
from ..sparse import issparse, csc_matrix, csr_matrix, coo_matrix, find
from ._group_columns import group_dense, group_sparse
EPS = np.finfo(np.float64).eps
def _adjust_scheme_to_bounds(x0, h, num_steps, scheme, lb, ub):
"""Adjust final difference scheme to the presence of bounds.
Parameters
----------
x0 : ndarray, shape (n,)
Point at which we wish to estimate derivative.
h : ndarray, shape (n,)
Desired finite difference steps.
num_steps : int
Number of `h` steps in one direction required to implement finite
difference scheme. For example, 2 means that we need to evaluate
f(x0 + 2 * h) or f(x0 - 2 * h)
scheme : {'1-sided', '2-sided'}
Whether steps in one or both directions are required. In other
words '1-sided' applies to forward and backward schemes, '2-sided'
applies to center schemes.
lb : ndarray, shape (n,)
Lower bounds on independent variables.
ub : ndarray, shape (n,)
Upper bounds on independent variables.
Returns
-------
h_adjusted : ndarray, shape (n,)
Adjusted step sizes. Step size decreases only if a sign flip or
switching to one-sided scheme doesn't allow to take a full step.
use_one_sided : ndarray of bool, shape (n,)
Whether to switch to one-sided scheme. Informative only for
``scheme='2-sided'``.
"""
if scheme == '1-sided':
use_one_sided = np.ones_like(h, dtype=bool)
elif scheme == '2-sided':
h = np.abs(h)
use_one_sided = np.zeros_like(h, dtype=bool)
else:
raise ValueError("`scheme` must be '1-sided' or '2-sided'.")
if np.all((lb == -np.inf) & (ub == np.inf)):
return h, use_one_sided
h_total = h * num_steps
h_adjusted = h.copy()
lower_dist = x0 - lb
upper_dist = ub - x0
if scheme == '1-sided':
x = x0 + h_total
violated = (x < lb) | (x > ub)
fitting = np.abs(h_total) <= np.maximum(lower_dist, upper_dist)
h_adjusted[violated & fitting] *= -1
forward = (upper_dist >= lower_dist) & ~fitting
h_adjusted[forward] = upper_dist[forward] / num_steps
backward = (upper_dist < lower_dist) & ~fitting
h_adjusted[backward] = -lower_dist[backward] / num_steps
elif scheme == '2-sided':
central = (lower_dist >= h_total) & (upper_dist >= h_total)
forward = (upper_dist >= lower_dist) & ~central
h_adjusted[forward] = np.minimum(
h[forward], 0.5 * upper_dist[forward] / num_steps)
use_one_sided[forward] = True
backward = (upper_dist < lower_dist) & ~central
h_adjusted[backward] = -np.minimum(
h[backward], 0.5 * lower_dist[backward] / num_steps)
use_one_sided[backward] = True
min_dist = np.minimum(upper_dist, lower_dist) / num_steps
adjusted_central = (~central & (np.abs(h_adjusted) <= min_dist))
h_adjusted[adjusted_central] = min_dist[adjusted_central]
use_one_sided[adjusted_central] = False
return h_adjusted, use_one_sided
relative_step = {"2-point": EPS**0.5,
"3-point": EPS**(1/3),
"cs": EPS**0.5}
def _compute_absolute_step(rel_step, x0, method):
if rel_step is None:
rel_step = relative_step[method]
sign_x0 = (x0 >= 0).astype(float) * 2 - 1
return rel_step * sign_x0 * np.maximum(1.0, np.abs(x0))
def _prepare_bounds(bounds, x0):
lb, ub = [np.asarray(b, dtype=float) for b in bounds]
if lb.ndim == 0:
lb = np.resize(lb, x0.shape)
if ub.ndim == 0:
ub = np.resize(ub, x0.shape)
return lb, ub
def group_columns(A, order=0):
"""Group columns of a 2-d matrix for sparse finite differencing [1]_.
Two columns are in the same group if in each row at least one of them
has zero. A greedy sequential algorithm is used to construct groups.
Parameters
----------
A : array_like or sparse matrix, shape (m, n)
Matrix of which to group columns.
order : int, iterable of int with shape (n,) or None
Permutation array which defines the order of columns enumeration.
If int or None, a random permutation is used with `order` used as
a random seed. Default is 0, that is use a random permutation but
guarantee repeatability.
Returns
-------
groups : ndarray of int, shape (n,)
Contains values from 0 to n_groups-1, where n_groups is the number
of found groups. Each value ``groups[i]`` is an index of a group to
which i-th column assigned. The procedure was helpful only if
n_groups is significantly less than n.
References
----------
.. [1] A. Curtis, M. J. D. Powell, and J. Reid, "On the estimation of
sparse Jacobian matrices", Journal of the Institute of Mathematics
and its Applications, 13 (1974), pp. 117-120.
"""
if issparse(A):
A = csc_matrix(A)
else:
A = np.atleast_2d(A)
A = (A != 0).astype(np.int32)
if A.ndim != 2:
raise ValueError("`A` must be 2-dimensional.")
m, n = A.shape
if order is None or np.isscalar(order):
rng = np.random.RandomState(order)
order = rng.permutation(n)
else:
order = np.asarray(order)
if order.shape != (n,):
raise ValueError("`order` has incorrect shape.")
A = A[:, order]
if issparse(A):
groups = group_sparse(m, n, A.indices, A.indptr)
else:
groups = group_dense(m, n, A)
groups[order] = groups.copy()
return groups
def approx_derivative(fun, x0, method='3-point', rel_step=None, f0=None,
bounds=(-np.inf, np.inf), sparsity=None,
as_linear_operator=False, args=(), kwargs={}):
"""Compute finite difference approximation of the derivatives of a
vector-valued function.
If a function maps from R^n to R^m, its derivatives form m-by-n matrix
called the Jacobian, where an element (i, j) is a partial derivative of
f[i] with respect to x[j].
Parameters
----------
fun : callable
Function of which to estimate the derivatives. The argument x
passed to this function is ndarray of shape (n,) (never a scalar
even if n=1). It must return 1-d array_like of shape (m,) or a scalar.
x0 : array_like of shape (n,) or float
Point at which to estimate the derivatives. Float will be converted
to a 1-d array.
method : {'3-point', '2-point', 'cs'}, optional
Finite difference method to use:
- '2-point' - use the first order accuracy forward or backward
difference.
- '3-point' - use central difference in interior points and the
second order accuracy forward or backward difference
near the boundary.
- 'cs' - use a complex-step finite difference scheme. This assumes
that the user function is real-valued and can be
analytically continued to the complex plane. Otherwise,
produces bogus results.
rel_step : None or array_like, optional
Relative step size to use. The absolute step size is computed as
``h = rel_step * sign(x0) * max(1, abs(x0))``, possibly adjusted to
fit into the bounds. For ``method='3-point'`` the sign of `h` is
ignored. If None (default) then step is selected automatically,
see Notes.
f0 : None or array_like, optional
If not None it is assumed to be equal to ``fun(x0)``, in this case
the ``fun(x0)`` is not called. Default is None.
bounds : tuple of array_like, optional
Lower and upper bounds on independent variables. Defaults to no bounds.
Each bound must match the size of `x0` or be a scalar, in the latter
case the bound will be the same for all variables. Use it to limit the
range of function evaluation. Bounds checking is not implemented
when `as_linear_operator` is True.
sparsity : {None, array_like, sparse matrix, 2-tuple}, optional
Defines a sparsity structure of the Jacobian matrix. If the Jacobian
matrix is known to have only few non-zero elements in each row, then
it's possible to estimate its several columns by a single function
evaluation [3]_. To perform such economic computations two ingredients
are required:
* structure : array_like or sparse matrix of shape (m, n). A zero
element means that a corresponding element of the Jacobian
identically equals to zero.
* groups : array_like of shape (n,). A column grouping for a given
sparsity structure, use `group_columns` to obtain it.
A single array or a sparse matrix is interpreted as a sparsity
structure, and groups are computed inside the function. A tuple is
interpreted as (structure, groups). If None (default), a standard
dense differencing will be used.
Note, that sparse differencing makes sense only for large Jacobian
matrices where each row contains few non-zero elements.
as_linear_operator : bool, optional
When True the function returns an `scipy.sparse.linalg.LinearOperator`.
Otherwise it returns a dense array or a sparse matrix depending on
`sparsity`. The linear operator provides an efficient way of computing
``J.dot(p)`` for any vector ``p`` of shape (n,), but does not allow
direct access to individual elements of the matrix. By default
`as_linear_operator` is False.
args, kwargs : tuple and dict, optional
Additional arguments passed to `fun`. Both empty by default.
The calling signature is ``fun(x, *args, **kwargs)``.
Returns
-------
J : {ndarray, sparse matrix, LinearOperator}
Finite difference approximation of the Jacobian matrix.
If `as_linear_operator` is True returns a LinearOperator
with shape (m, n). Otherwise it returns a dense array or sparse
matrix depending on how `sparsity` is defined. If `sparsity`
is None then a ndarray with shape (m, n) is returned. If
`sparsity` is not None returns a csr_matrix with shape (m, n).
For sparse matrices and linear operators it is always returned as
a 2-dimensional structure, for ndarrays, if m=1 it is returned
as a 1-dimensional gradient array with shape (n,).
See Also
--------
check_derivative : Check correctness of a function computing derivatives.
Notes
-----
If `rel_step` is not provided, it assigned to ``EPS**(1/s)``, where EPS is
machine epsilon for float64 numbers, s=2 for '2-point' method and s=3 for
'3-point' method. Such relative step approximately minimizes a sum of
truncation and round-off errors, see [1]_.
A finite difference scheme for '3-point' method is selected automatically.
The well-known central difference scheme is used for points sufficiently
far from the boundary, and 3-point forward or backward scheme is used for
points near the boundary. Both schemes have the second-order accuracy in
terms of Taylor expansion. Refer to [2]_ for the formulas of 3-point
forward and backward difference schemes.
For dense differencing when m=1 Jacobian is returned with a shape (n,),
on the other hand when n=1 Jacobian is returned with a shape (m, 1).
Our motivation is the following: a) It handles a case of gradient
computation (m=1) in a conventional way. b) It clearly separates these two
different cases. b) In all cases np.atleast_2d can be called to get 2-d
Jacobian with correct dimensions.
References
----------
.. [1] W. H. Press et. al. "Numerical Recipes. The Art of Scientific
Computing. 3rd edition", sec. 5.7.
.. [2] A. Curtis, M. J. D. Powell, and J. Reid, "On the estimation of
sparse Jacobian matrices", Journal of the Institute of Mathematics
and its Applications, 13 (1974), pp. 117-120.
.. [3] B. Fornberg, "Generation of Finite Difference Formulas on
Arbitrarily Spaced Grids", Mathematics of Computation 51, 1988.
Examples
--------
>>> import numpy as np
>>> from scipy.optimize import approx_derivative
>>>
>>> def f(x, c1, c2):
... return np.array([x[0] * np.sin(c1 * x[1]),
... x[0] * np.cos(c2 * x[1])])
...
>>> x0 = np.array([1.0, 0.5 * np.pi])
>>> approx_derivative(f, x0, args=(1, 2))
array([[ 1., 0.],
[-1., 0.]])
Bounds can be used to limit the region of function evaluation.
In the example below we compute left and right derivative at point 1.0.
>>> def g(x):
... return x**2 if x >= 1 else x
...
>>> x0 = 1.0
>>> approx_derivative(g, x0, bounds=(-np.inf, 1.0))
array([ 1.])
>>> approx_derivative(g, x0, bounds=(1.0, np.inf))
array([ 2.])
"""
if method not in ['2-point', '3-point', 'cs']:
raise ValueError("Unknown method '%s'. " % method)
x0 = np.atleast_1d(x0)
if x0.ndim > 1:
raise ValueError("`x0` must have at most 1 dimension.")
lb, ub = _prepare_bounds(bounds, x0)
if lb.shape != x0.shape or ub.shape != x0.shape:
raise ValueError("Inconsistent shapes between bounds and `x0`.")
if as_linear_operator and not (np.all(np.isinf(lb))
and np.all(np.isinf(ub))):
raise ValueError("Bounds not supported when "
"`as_linear_operator` is True.")
def fun_wrapped(x):
f = np.atleast_1d(fun(x, *args, **kwargs))
if f.ndim > 1:
raise RuntimeError("`fun` return value has "
"more than 1 dimension.")
return f
if f0 is None:
f0 = fun_wrapped(x0)
else:
f0 = np.atleast_1d(f0)
if f0.ndim > 1:
raise ValueError("`f0` passed has more than 1 dimension.")
if np.any((x0 < lb) | (x0 > ub)):
raise ValueError("`x0` violates bound constraints.")
if as_linear_operator:
if rel_step is None:
rel_step = relative_step[method]
return _linear_operator_difference(fun_wrapped, x0,
f0, rel_step, method)
else:
h = _compute_absolute_step(rel_step, x0, method)
if method == '2-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '1-sided', lb, ub)
elif method == '3-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '2-sided', lb, ub)
elif method == 'cs':
use_one_sided = False
if sparsity is None:
return _dense_difference(fun_wrapped, x0, f0, h,
use_one_sided, method)
else:
if not issparse(sparsity) and len(sparsity) == 2:
structure, groups = sparsity
else:
structure = sparsity
groups = group_columns(sparsity)
if issparse(structure):
structure = csc_matrix(structure)
else:
structure = np.atleast_2d(structure)
groups = np.atleast_1d(groups)
return _sparse_difference(fun_wrapped, x0, f0, h,
use_one_sided, structure,
groups, method)
def _linear_operator_difference(fun, x0, f0, h, method):
m = f0.size
n = x0.size
if method == '2-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / norm(p)
x = x0 + dx*p
df = fun(x) - f0
return df / dx
elif method == '3-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = 2*h / norm(p)
x1 = x0 - (dx/2)*p
x2 = x0 + (dx/2)*p
f1 = fun(x1)
f2 = fun(x2)
df = f2 - f1
return df / dx
elif method == 'cs':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / norm(p)
x = x0 + dx*p*1.j
f1 = fun(x)
df = f1.imag
return df / dx
else:
raise RuntimeError("Never be here.")
return LinearOperator((m, n), matvec)
def _dense_difference(fun, x0, f0, h, use_one_sided, method):
m = f0.size
n = x0.size
J_transposed = np.empty((n, m))
h_vecs = np.diag(h)
for i in range(h.size):
if method == '2-point':
x = x0 + h_vecs[i]
dx = x[i] - x0[i] # Recompute dx as exactly representable number.
df = fun(x) - f0
elif method == '3-point' and use_one_sided[i]:
x1 = x0 + h_vecs[i]
x2 = x0 + 2 * h_vecs[i]
dx = x2[i] - x0[i]
f1 = fun(x1)
f2 = fun(x2)
df = -3.0 * f0 + 4 * f1 - f2
elif method == '3-point' and not use_one_sided[i]:
x1 = x0 - h_vecs[i]
x2 = x0 + h_vecs[i]
dx = x2[i] - x1[i]
f1 = fun(x1)
f2 = fun(x2)
df = f2 - f1
elif method == 'cs':
f1 = fun(x0 + h_vecs[i]*1.j)
df = f1.imag
dx = h_vecs[i, i]
else:
raise RuntimeError("Never be here.")
J_transposed[i] = df / dx
if m == 1:
J_transposed = np.ravel(J_transposed)
return J_transposed.T
def _sparse_difference(fun, x0, f0, h, use_one_sided,
structure, groups, method):
m = f0.size
n = x0.size
row_indices = []
col_indices = []
fractions = []
n_groups = np.max(groups) + 1
for group in range(n_groups):
# Perturb variables which are in the same group simultaneously.
e = np.equal(group, groups)
h_vec = h * e
if method == '2-point':
x = x0 + h_vec
dx = x - x0
df = fun(x) - f0
# The result is written to columns which correspond to perturbed
# variables.
cols, = np.nonzero(e)
# Find all non-zero elements in selected columns of Jacobian.
i, j, _ = find(structure[:, cols])
# Restore column indices in the full array.
j = cols[j]
elif method == '3-point':
# Here we do conceptually the same but separate one-sided
# and two-sided schemes.
x1 = x0.copy()
x2 = x0.copy()
mask_1 = use_one_sided & e
x1[mask_1] += h_vec[mask_1]
x2[mask_1] += 2 * h_vec[mask_1]
mask_2 = ~use_one_sided & e
x1[mask_2] -= h_vec[mask_2]
x2[mask_2] += h_vec[mask_2]
dx = np.zeros(n)
dx[mask_1] = x2[mask_1] - x0[mask_1]
dx[mask_2] = x2[mask_2] - x1[mask_2]
f1 = fun(x1)
f2 = fun(x2)
cols, = np.nonzero(e)
i, j, _ = find(structure[:, cols])
j = cols[j]
mask = use_one_sided[j]
df = np.empty(m)
rows = i[mask]
df[rows] = -3 * f0[rows] + 4 * f1[rows] - f2[rows]
rows = i[~mask]
df[rows] = f2[rows] - f1[rows]
elif method == 'cs':
f1 = fun(x0 + h_vec*1.j)
df = f1.imag
dx = h_vec
cols, = np.nonzero(e)
i, j, _ = find(structure[:, cols])
j = cols[j]
else:
raise ValueError("Never be here.")
# All that's left is to compute the fraction. We store i, j and
# fractions as separate arrays and later construct coo_matrix.
row_indices.append(i)
col_indices.append(j)
fractions.append(df[i] / dx[j])
row_indices = np.hstack(row_indices)
col_indices = np.hstack(col_indices)
fractions = np.hstack(fractions)
J = coo_matrix((fractions, (row_indices, col_indices)), shape=(m, n))
return csr_matrix(J)
def check_derivative(fun, jac, x0, bounds=(-np.inf, np.inf), args=(),
kwargs={}):
"""Check correctness of a function computing derivatives (Jacobian or
gradient) by comparison with a finite difference approximation.
Parameters
----------
fun : callable
Function of which to estimate the derivatives. The argument x
passed to this function is ndarray of shape (n,) (never a scalar
even if n=1). It must return 1-d array_like of shape (m,) or a scalar.
jac : callable
Function which computes Jacobian matrix of `fun`. It must work with
argument x the same way as `fun`. The return value must be array_like
or sparse matrix with an appropriate shape.
x0 : array_like of shape (n,) or float
Point at which to estimate the derivatives. Float will be converted
to 1-d array.
bounds : 2-tuple of array_like, optional
Lower and upper bounds on independent variables. Defaults to no bounds.
Each bound must match the size of `x0` or be a scalar, in the latter
case the bound will be the same for all variables. Use it to limit the
range of function evaluation.
args, kwargs : tuple and dict, optional
Additional arguments passed to `fun` and `jac`. Both empty by default.
The calling signature is ``fun(x, *args, **kwargs)`` and the same
for `jac`.
Returns
-------
accuracy : float
The maximum among all relative errors for elements with absolute values
higher than 1 and absolute errors for elements with absolute values
less or equal than 1. If `accuracy` is on the order of 1e-6 or lower,
then it is likely that your `jac` implementation is correct.
See Also
--------
approx_derivative : Compute finite difference approximation of derivative.
Examples
--------
>>> import numpy as np
>>> from scipy.optimize import check_derivative
>>>
>>>
>>> def f(x, c1, c2):
... return np.array([x[0] * np.sin(c1 * x[1]),
... x[0] * np.cos(c2 * x[1])])
...
>>> def jac(x, c1, c2):
... return np.array([
... [np.sin(c1 * x[1]), c1 * x[0] * np.cos(c1 * x[1])],
... [np.cos(c2 * x[1]), -c2 * x[0] * np.sin(c2 * x[1])]
... ])
...
>>>
>>> x0 = np.array([1.0, 0.5 * np.pi])
>>> check_derivative(f, jac, x0, args=(1, 2))
2.4492935982947064e-16
"""
J_to_test = jac(x0, *args, **kwargs)
if issparse(J_to_test):
J_diff = approx_derivative(fun, x0, bounds=bounds, sparsity=J_to_test,
args=args, kwargs=kwargs)
J_to_test = csr_matrix(J_to_test)
abs_err = J_to_test - J_diff
i, j, abs_err_data = find(abs_err)
J_diff_data = np.asarray(J_diff[i, j]).ravel()
return np.max(np.abs(abs_err_data) /
np.maximum(1, np.abs(J_diff_data)))
else:
J_diff = approx_derivative(fun, x0, bounds=bounds,
args=args, kwargs=kwargs)
abs_err = np.abs(J_to_test - J_diff)
return np.max(abs_err / np.maximum(1, np.abs(J_diff)))
| 23,753 | 36.115625 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_hessian_update_strategy.py
|
"""Hessian update strategies for quasi-Newton optimization methods."""
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.linalg import norm
from scipy.linalg import get_blas_funcs
from warnings import warn
__all__ = ['HessianUpdateStrategy', 'BFGS', 'SR1']
class HessianUpdateStrategy(object):
"""Interface for implementing Hessian update strategies.
Many optimization methods make use of Hessian (or inverse Hessian)
approximations, such as the quasi-Newton methods BFGS, SR1, L-BFGS.
Some of these approximations, however, do not actually need to store
the entire matrix or can compute the internal matrix product with a
given vector in a very efficiently manner. This class serves as an
abstract interface between the optimization algorithm and the
quasi-Newton update strategies, giving freedom of implementation
to store and update the internal matrix as efficiently as possible.
Different choices of initialization and update procedure will result
in different quasi-Newton strategies.
Four methods should be implemented in derived classes: ``initialize``,
``update``, ``dot`` and ``get_matrix``.
Notes
-----
Any instance of a class that implements this interface,
can be accepted by the method ``minimize`` and used by
the compatible solvers to approximate the Hessian (or
inverse Hessian) used by the optimization algorithms.
"""
def initialize(self, n, approx_type):
"""Initialize internal matrix.
Allocate internal memory for storing and updating
the Hessian or its inverse.
Parameters
----------
n : int
Problem dimension.
approx_type : {'hess', 'inv_hess'}
Selects either the Hessian or the inverse Hessian.
When set to 'hess' the Hessian will be stored and updated.
When set to 'inv_hess' its inverse will be used instead.
"""
raise NotImplementedError("The method ``initialize(n, approx_type)``"
" is not implemented.")
def update(self, delta_x, delta_grad):
"""Update internal matrix.
Update Hessian matrix or its inverse (depending on how 'approx_type'
is defined) using information about the last evaluated points.
Parameters
----------
delta_x : ndarray
The difference between two points the gradient
function have been evaluated at: ``delta_x = x2 - x1``.
delta_grad : ndarray
The difference between the gradients:
``delta_grad = grad(x2) - grad(x1)``.
"""
raise NotImplementedError("The method ``update(delta_x, delta_grad)``"
" is not implemented.")
def dot(self, p):
"""Compute the product of the internal matrix with the given vector.
Parameters
----------
p : array_like
1-d array representing a vector.
Returns
-------
Hp : array
1-d represents the result of multiplying the approximation matrix
by vector p.
"""
raise NotImplementedError("The method ``dot(p)``"
" is not implemented.")
def get_matrix(self):
"""Return current internal matrix.
Returns
-------
H : ndarray, shape (n, n)
Dense matrix containing either the Hessian
or its inverse (depending on how 'approx_type'
is defined).
"""
raise NotImplementedError("The method ``get_matrix(p)``"
" is not implemented.")
class FullHessianUpdateStrategy(HessianUpdateStrategy):
"""Hessian update strategy with full dimensional internal representation.
"""
_syr = get_blas_funcs('syr', dtype='d') # Symmetric rank 1 update
_syr2 = get_blas_funcs('syr2', dtype='d') # Symmetric rank 2 update
# Symmetric matrix-vector product
_symv = get_blas_funcs('symv', dtype='d')
def __init__(self, init_scale='auto'):
self.init_scale = init_scale
# Until initialize is called we can't really use the class,
# so it makes sense to set everything to None.
self.first_iteration = None
self.approx_type = None
self.B = None
self.H = None
def initialize(self, n, approx_type):
"""Initialize internal matrix.
Allocate internal memory for storing and updating
the Hessian or its inverse.
Parameters
----------
n : int
Problem dimension.
approx_type : {'hess', 'inv_hess'}
Selects either the Hessian or the inverse Hessian.
When set to 'hess' the Hessian will be stored and updated.
When set to 'inv_hess' its inverse will be used instead.
"""
self.first_iteration = True
self.n = n
self.approx_type = approx_type
if approx_type not in ('hess', 'inv_hess'):
raise ValueError("`approx_type` must be 'hess' or 'inv_hess'.")
# Create matrix
if self.approx_type == 'hess':
self.B = np.eye(n, dtype=float)
else:
self.H = np.eye(n, dtype=float)
def _auto_scale(self, delta_x, delta_grad):
# Heuristic to scale matrix at first iteration.
# Described in Nocedal and Wright "Numerical Optimization"
# p.143 formula (6.20).
s_norm2 = np.dot(delta_x, delta_x)
y_norm2 = np.dot(delta_grad, delta_grad)
ys = np.abs(np.dot(delta_grad, delta_x))
if ys == 0.0 or y_norm2 == 0 or s_norm2 == 0:
return 1
if self.approx_type == 'hess':
return y_norm2 / ys
else:
return ys / y_norm2
def _update_implementation(self, delta_x, delta_grad):
raise NotImplementedError("The method ``_update_implementation``"
" is not implemented.")
def update(self, delta_x, delta_grad):
"""Update internal matrix.
Update Hessian matrix or its inverse (depending on how 'approx_type'
is defined) using information about the last evaluated points.
Parameters
----------
delta_x : ndarray
The difference between two points the gradient
function have been evaluated at: ``delta_x = x2 - x1``.
delta_grad : ndarray
The difference between the gradients:
``delta_grad = grad(x2) - grad(x1)``.
"""
if np.all(delta_x == 0.0):
return
if np.all(delta_grad == 0.0):
warn('delta_grad == 0.0. Check if the approximated '
'function is linear. If the function is linear '
'better results can be obtained by defining the '
'Hessian as zero instead of using quasi-Newton '
'approximations.', UserWarning)
return
if self.first_iteration:
# Get user specific scale
if self.init_scale == "auto":
scale = self._auto_scale(delta_x, delta_grad)
else:
scale = float(self.init_scale)
# Scale initial matrix with ``scale * np.eye(n)``
if self.approx_type == 'hess':
self.B *= scale
else:
self.H *= scale
self.first_iteration = False
self._update_implementation(delta_x, delta_grad)
def dot(self, p):
"""Compute the product of the internal matrix with the given vector.
Parameters
----------
p : array_like
1-d array representing a vector.
Returns
-------
Hp : array
1-d represents the result of multiplying the approximation matrix
by vector p.
"""
if self.approx_type == 'hess':
return self._symv(1, self.B, p)
else:
return self._symv(1, self.H, p)
def get_matrix(self):
"""Return the current internal matrix.
Returns
-------
M : ndarray, shape (n, n)
Dense matrix containing either the Hessian or its inverse
(depending on how `approx_type` was defined).
"""
if self.approx_type == 'hess':
M = np.copy(self.B)
else:
M = np.copy(self.H)
li = np.tril_indices_from(M, k=-1)
M[li] = M.T[li]
return M
class BFGS(FullHessianUpdateStrategy):
"""Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy.
Parameters
----------
exception_strategy : {'skip_update', 'damp_update'}, optional
Define how to proceed when the curvature condition is violated.
Set it to 'skip_update' to just skip the update. Or, alternatively,
set it to 'damp_update' to interpolate between the actual BFGS
result and the unmodified matrix. Both exceptions strategies
are explained in [1]_, p.536-537.
min_curvature : float
This number, scaled by a normalization factor, defines the
minimum curvature ``dot(delta_grad, delta_x)`` allowed to go
unaffected by the exception strategy. By default is equal to
1e-8 when ``exception_strategy = 'skip_update'`` and equal
to 0.2 when ``exception_strategy = 'damp_update'``.
init_scale : {float, 'auto'}
Matrix scale at first iteration. At the first
iteration the Hessian matrix or its inverse will be initialized
with ``init_scale*np.eye(n)``, where ``n`` is the problem dimension.
Set it to 'auto' in order to use an automatic heuristic for choosing
the initial scale. The heuristic is described in [1]_, p.143.
By default uses 'auto'.
Notes
-----
The update is based on the description in [1]_, p.140.
References
----------
.. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
Second Edition (2006).
"""
def __init__(self, exception_strategy='skip_update', min_curvature=None,
init_scale='auto'):
if exception_strategy == 'skip_update':
if min_curvature is not None:
self.min_curvature = min_curvature
else:
self.min_curvature = 1e-8
elif exception_strategy == 'damp_update':
if min_curvature is not None:
self.min_curvature = min_curvature
else:
self.min_curvature = 0.2
else:
raise ValueError("`exception_strategy` must be 'skip_update' "
"or 'damp_update'.")
super(BFGS, self).__init__(init_scale)
self.exception_strategy = exception_strategy
def _update_inverse_hessian(self, ys, Hy, yHy, s):
"""Update the inverse Hessian matrix.
BFGS update using the formula:
``H <- H + ((H*y).T*y + s.T*y)/(s.T*y)^2 * (s*s.T)
- 1/(s.T*y) * ((H*y)*s.T + s*(H*y).T)``
where ``s = delta_x`` and ``y = delta_grad``. This formula is
equivalent to (6.17) in [1]_ written in a more efficient way
for implementation.
References
----------
.. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
Second Edition (2006).
"""
self.H = self._syr2(-1.0 / ys, s, Hy, a=self.H)
self.H = self._syr((ys+yHy)/ys**2, s, a=self.H)
def _update_hessian(self, ys, Bs, sBs, y):
"""Update the Hessian matrix.
BFGS update using the formula:
``B <- B - (B*s)*(B*s).T/s.T*(B*s) + y*y^T/s.T*y``
where ``s`` is short for ``delta_x`` and ``y`` is short
for ``delta_grad``. Formula (6.19) in [1]_.
References
----------
.. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
Second Edition (2006).
"""
self.B = self._syr(1.0 / ys, y, a=self.B)
self.B = self._syr(-1.0 / sBs, Bs, a=self.B)
def _update_implementation(self, delta_x, delta_grad):
# Auxiliary variables w and z
if self.approx_type == 'hess':
w = delta_x
z = delta_grad
else:
w = delta_grad
z = delta_x
# Do some common operations
wz = np.dot(w, z)
Mw = self.dot(w)
wMw = Mw.dot(w)
# Guarantee that wMw > 0 by reinitializing matrix.
# While this is always true in exact arithmetics,
# indefinite matrix may appear due to roundoff errors.
if wMw <= 0.0:
scale = self._auto_scale(delta_x, delta_grad)
# Reinitialize matrix
if self.approx_type == 'hess':
self.B = scale * np.eye(self.n, dtype=float)
else:
self.H = scale * np.eye(self.n, dtype=float)
# Do common operations for new matrix
Mw = self.dot(w)
wMw = Mw.dot(w)
# Check if curvature condition is violated
if wz <= self.min_curvature * wMw:
# If the option 'skip_update' is set
# we just skip the update when the condion
# is violated.
if self.exception_strategy == 'skip_update':
return
# If the option 'damp_update' is set we
# interpolate between the actual BFGS
# result and the unmodified matrix.
elif self.exception_strategy == 'damp_update':
update_factor = (1-self.min_curvature) / (1 - wz/wMw)
z = update_factor*z + (1-update_factor)*Mw
wz = np.dot(w, z)
# Update matrix
if self.approx_type == 'hess':
self._update_hessian(wz, Mw, wMw, z)
else:
self._update_inverse_hessian(wz, Mw, wMw, z)
class SR1(FullHessianUpdateStrategy):
"""Symmetric-rank-1 Hessian update strategy.
Parameters
----------
min_denominator : float
This number, scaled by a normalization factor,
defines the minimum denominator magnitude allowed
in the update. When the condition is violated we skip
the update. By default uses ``1e-8``.
init_scale : {float, 'auto'}, optional
Matrix scale at first iteration. At the first
iteration the Hessian matrix or its inverse will be initialized
with ``init_scale*np.eye(n)``, where ``n`` is the problem dimension.
Set it to 'auto' in order to use an automatic heuristic for choosing
the initial scale. The heuristic is described in [1]_, p.143.
By default uses 'auto'.
Notes
-----
The update is based on the description in [1]_, p.144-146.
References
----------
.. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
Second Edition (2006).
"""
def __init__(self, min_denominator=1e-8, init_scale='auto'):
self.min_denominator = min_denominator
super(SR1, self).__init__(init_scale)
def _update_implementation(self, delta_x, delta_grad):
# Auxiliary variables w and z
if self.approx_type == 'hess':
w = delta_x
z = delta_grad
else:
w = delta_grad
z = delta_x
# Do some common operations
Mw = self.dot(w)
z_minus_Mw = z - Mw
denominator = np.dot(w, z_minus_Mw)
# If the denominator is too small
# we just skip the update.
if np.abs(denominator) <= self.min_denominator*norm(w)*norm(z_minus_Mw):
return
# Update matrix
if self.approx_type == 'hess':
self.B = self._syr(1/denominator, z_minus_Mw, a=self.B)
else:
self.H = self._syr(1/denominator, z_minus_Mw, a=self.H)
| 15,924 | 35.948956 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/zeros.py
|
from __future__ import division, print_function, absolute_import
import warnings
from . import _zeros
from numpy import finfo, sign, sqrt
_iter = 100
_xtol = 2e-12
_rtol = 4*finfo(float).eps
__all__ = ['newton', 'bisect', 'ridder', 'brentq', 'brenth']
CONVERGED = 'converged'
SIGNERR = 'sign error'
CONVERR = 'convergence error'
flag_map = {0: CONVERGED, -1: SIGNERR, -2: CONVERR}
class RootResults(object):
""" Represents the root finding result.
Attributes
----------
root : float
Estimated root location.
iterations : int
Number of iterations needed to find the root.
function_calls : int
Number of times the function was called.
converged : bool
True if the routine converged.
flag : str
Description of the cause of termination.
"""
def __init__(self, root, iterations, function_calls, flag):
self.root = root
self.iterations = iterations
self.function_calls = function_calls
self.converged = flag == 0
try:
self.flag = flag_map[flag]
except KeyError:
self.flag = 'unknown error %d' % (flag,)
def __repr__(self):
attrs = ['converged', 'flag', 'function_calls',
'iterations', 'root']
m = max(map(len, attrs)) + 1
return '\n'.join([a.rjust(m) + ': ' + repr(getattr(self, a))
for a in attrs])
def results_c(full_output, r):
if full_output:
x, funcalls, iterations, flag = r
results = RootResults(root=x,
iterations=iterations,
function_calls=funcalls,
flag=flag)
return x, results
else:
return r
# Newton-Raphson method
def newton(func, x0, fprime=None, args=(), tol=1.48e-8, maxiter=50,
fprime2=None):
"""
Find a zero using the Newton-Raphson or secant method.
Find a zero of the function `func` given a nearby starting point `x0`.
The Newton-Raphson method is used if the derivative `fprime` of `func`
is provided, otherwise the secant method is used. If the second order
derivative `fprime2` of `func` is provided, then Halley's method is used.
Parameters
----------
func : function
The function whose zero is wanted. It must be a function of a
single variable of the form f(x,a,b,c...), where a,b,c... are extra
arguments that can be passed in the `args` parameter.
x0 : float
An initial estimate of the zero that should be somewhere near the
actual zero.
fprime : function, optional
The derivative of the function when available and convenient. If it
is None (default), then the secant method is used.
args : tuple, optional
Extra arguments to be used in the function call.
tol : float, optional
The allowable error of the zero value.
maxiter : int, optional
Maximum number of iterations.
fprime2 : function, optional
The second order derivative of the function when available and
convenient. If it is None (default), then the normal Newton-Raphson
or the secant method is used. If it is not None, then Halley's method
is used.
Returns
-------
zero : float
Estimated location where function is zero.
See Also
--------
brentq, brenth, ridder, bisect
fsolve : find zeroes in n dimensions.
Notes
-----
The convergence rate of the Newton-Raphson method is quadratic,
the Halley method is cubic, and the secant method is
sub-quadratic. This means that if the function is well behaved
the actual error in the estimated zero is approximately the square
(cube for Halley) of the requested tolerance up to roundoff
error. However, the stopping criterion used here is the step size
and there is no guarantee that a zero has been found. Consequently
the result should be verified. Safer algorithms are brentq,
brenth, ridder, and bisect, but they all require that the root
first be bracketed in an interval where the function changes
sign. The brentq algorithm is recommended for general use in one
dimensional problems when such an interval has been found.
Examples
--------
>>> def f(x):
... return (x**3 - 1) # only one real root at x = 1
>>> from scipy import optimize
``fprime`` not provided, use secant method
>>> root = optimize.newton(f, 1.5)
>>> root
1.0000000000000016
>>> root = optimize.newton(f, 1.5, fprime2=lambda x: 6 * x)
>>> root
1.0000000000000016
Only ``fprime`` provided, use Newton Raphson method
>>> root = optimize.newton(f, 1.5, fprime=lambda x: 3 * x**2)
>>> root
1.0
Both ``fprime2`` and ``fprime`` provided, use Halley's method
>>> root = optimize.newton(f, 1.5, fprime=lambda x: 3 * x**2,
... fprime2=lambda x: 6 * x)
>>> root
1.0
"""
if tol <= 0:
raise ValueError("tol too small (%g <= 0)" % tol)
if maxiter < 1:
raise ValueError("maxiter must be greater than 0")
# Multiply by 1.0 to convert to floating point. We don't use float(x0)
# so it still works if x0 is complex.
p0 = 1.0 * x0
if fprime is not None:
# Newton-Rapheson method
for iter in range(maxiter):
fder = fprime(p0, *args)
if fder == 0:
msg = "derivative was zero."
warnings.warn(msg, RuntimeWarning)
return p0
fval = func(p0, *args)
newton_step = fval / fder
if fprime2 is None:
# Newton step
p = p0 - newton_step
else:
fder2 = fprime2(p0, *args)
# Halley's method
p = p0 - newton_step / (1.0 - 0.5 * newton_step * fder2 / fder)
if abs(p - p0) < tol:
return p
p0 = p
else:
# Secant method
if x0 >= 0:
p1 = x0*(1 + 1e-4) + 1e-4
else:
p1 = x0*(1 + 1e-4) - 1e-4
q0 = func(p0, *args)
q1 = func(p1, *args)
for iter in range(maxiter):
if q1 == q0:
if p1 != p0:
msg = "Tolerance of %s reached" % (p1 - p0)
warnings.warn(msg, RuntimeWarning)
return (p1 + p0)/2.0
else:
p = p1 - q1*(p1 - p0)/(q1 - q0)
if abs(p - p1) < tol:
return p
p0 = p1
q0 = q1
p1 = p
q1 = func(p1, *args)
msg = "Failed to converge after %d iterations, value is %s" % (maxiter, p)
raise RuntimeError(msg)
def bisect(f, a, b, args=(),
xtol=_xtol, rtol=_rtol, maxiter=_iter,
full_output=False, disp=True):
"""
Find root of a function within an interval.
Basic bisection routine to find a zero of the function `f` between the
arguments `a` and `b`. `f(a)` and `f(b)` cannot have the same signs.
Slow but sure.
Parameters
----------
f : function
Python function returning a number. `f` must be continuous, and
f(a) and f(b) must have opposite signs.
a : number
One end of the bracketing interval [a,b].
b : number
The other end of the bracketing interval [a,b].
xtol : number, optional
The computed root ``x0`` will satisfy ``np.allclose(x, x0,
atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
parameter must be nonnegative.
rtol : number, optional
The computed root ``x0`` will satisfy ``np.allclose(x, x0,
atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
parameter cannot be smaller than its default value of
``4*np.finfo(float).eps``.
maxiter : number, optional
if convergence is not achieved in `maxiter` iterations, an error is
raised. Must be >= 0.
args : tuple, optional
containing extra arguments for the function `f`.
`f` is called by ``apply(f, (x)+args)``.
full_output : bool, optional
If `full_output` is False, the root is returned. If `full_output` is
True, the return value is ``(x, r)``, where x is the root, and r is
a `RootResults` object.
disp : bool, optional
If True, raise RuntimeError if the algorithm didn't converge.
Returns
-------
x0 : float
Zero of `f` between `a` and `b`.
r : RootResults (present if ``full_output = True``)
Object containing information about the convergence. In particular,
``r.converged`` is True if the routine converged.
Examples
--------
>>> def f(x):
... return (x**2 - 1)
>>> from scipy import optimize
>>> root = optimize.bisect(f, 0, 2)
>>> root
1.0
>>> root = optimize.bisect(f, -2, 0)
>>> root
-1.0
See Also
--------
brentq, brenth, bisect, newton
fixed_point : scalar fixed-point finder
fsolve : n-dimensional root-finding
"""
if not isinstance(args, tuple):
args = (args,)
if xtol <= 0:
raise ValueError("xtol too small (%g <= 0)" % xtol)
if rtol < _rtol:
raise ValueError("rtol too small (%g < %g)" % (rtol, _rtol))
r = _zeros._bisect(f,a,b,xtol,rtol,maxiter,args,full_output,disp)
return results_c(full_output, r)
def ridder(f, a, b, args=(),
xtol=_xtol, rtol=_rtol, maxiter=_iter,
full_output=False, disp=True):
"""
Find a root of a function in an interval.
Parameters
----------
f : function
Python function returning a number. f must be continuous, and f(a) and
f(b) must have opposite signs.
a : number
One end of the bracketing interval [a,b].
b : number
The other end of the bracketing interval [a,b].
xtol : number, optional
The computed root ``x0`` will satisfy ``np.allclose(x, x0,
atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
parameter must be nonnegative.
rtol : number, optional
The computed root ``x0`` will satisfy ``np.allclose(x, x0,
atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
parameter cannot be smaller than its default value of
``4*np.finfo(float).eps``.
maxiter : number, optional
if convergence is not achieved in maxiter iterations, an error is
raised. Must be >= 0.
args : tuple, optional
containing extra arguments for the function `f`.
`f` is called by ``apply(f, (x)+args)``.
full_output : bool, optional
If `full_output` is False, the root is returned. If `full_output` is
True, the return value is ``(x, r)``, where `x` is the root, and `r` is
a RootResults object.
disp : bool, optional
If True, raise RuntimeError if the algorithm didn't converge.
Returns
-------
x0 : float
Zero of `f` between `a` and `b`.
r : RootResults (present if ``full_output = True``)
Object containing information about the convergence.
In particular, ``r.converged`` is True if the routine converged.
See Also
--------
brentq, brenth, bisect, newton : one-dimensional root-finding
fixed_point : scalar fixed-point finder
Notes
-----
Uses [Ridders1979]_ method to find a zero of the function `f` between the
arguments `a` and `b`. Ridders' method is faster than bisection, but not
generally as fast as the Brent routines. [Ridders1979]_ provides the
classic description and source of the algorithm. A description can also be
found in any recent edition of Numerical Recipes.
The routine used here diverges slightly from standard presentations in
order to be a bit more careful of tolerance.
Examples
--------
>>> def f(x):
... return (x**2 - 1)
>>> from scipy import optimize
>>> root = optimize.ridder(f, 0, 2)
>>> root
1.0
>>> root = optimize.ridder(f, -2, 0)
>>> root
-1.0
References
----------
.. [Ridders1979]
Ridders, C. F. J. "A New Algorithm for Computing a
Single Root of a Real Continuous Function."
IEEE Trans. Circuits Systems 26, 979-980, 1979.
"""
if not isinstance(args, tuple):
args = (args,)
if xtol <= 0:
raise ValueError("xtol too small (%g <= 0)" % xtol)
if rtol < _rtol:
raise ValueError("rtol too small (%g < %g)" % (rtol, _rtol))
r = _zeros._ridder(f,a,b,xtol,rtol,maxiter,args,full_output,disp)
return results_c(full_output, r)
def brentq(f, a, b, args=(),
xtol=_xtol, rtol=_rtol, maxiter=_iter,
full_output=False, disp=True):
"""
Find a root of a function in a bracketing interval using Brent's method.
Uses the classic Brent's method to find a zero of the function `f` on
the sign changing interval [a , b]. Generally considered the best of the
rootfinding routines here. It is a safe version of the secant method that
uses inverse quadratic extrapolation. Brent's method combines root
bracketing, interval bisection, and inverse quadratic interpolation. It is
sometimes known as the van Wijngaarden-Dekker-Brent method. Brent (1973)
claims convergence is guaranteed for functions computable within [a,b].
[Brent1973]_ provides the classic description of the algorithm. Another
description can be found in a recent edition of Numerical Recipes, including
[PressEtal1992]_. Another description is at
http://mathworld.wolfram.com/BrentsMethod.html. It should be easy to
understand the algorithm just by reading our code. Our code diverges a bit
from standard presentations: we choose a different formula for the
extrapolation step.
Parameters
----------
f : function
Python function returning a number. The function :math:`f`
must be continuous, and :math:`f(a)` and :math:`f(b)` must
have opposite signs.
a : number
One end of the bracketing interval :math:`[a, b]`.
b : number
The other end of the bracketing interval :math:`[a, b]`.
xtol : number, optional
The computed root ``x0`` will satisfy ``np.allclose(x, x0,
atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
parameter must be nonnegative. For nice functions, Brent's
method will often satisfy the above condition with ``xtol/2``
and ``rtol/2``. [Brent1973]_
rtol : number, optional
The computed root ``x0`` will satisfy ``np.allclose(x, x0,
atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
parameter cannot be smaller than its default value of
``4*np.finfo(float).eps``. For nice functions, Brent's
method will often satisfy the above condition with ``xtol/2``
and ``rtol/2``. [Brent1973]_
maxiter : number, optional
if convergence is not achieved in maxiter iterations, an error is
raised. Must be >= 0.
args : tuple, optional
containing extra arguments for the function `f`.
`f` is called by ``apply(f, (x)+args)``.
full_output : bool, optional
If `full_output` is False, the root is returned. If `full_output` is
True, the return value is ``(x, r)``, where `x` is the root, and `r` is
a RootResults object.
disp : bool, optional
If True, raise RuntimeError if the algorithm didn't converge.
Returns
-------
x0 : float
Zero of `f` between `a` and `b`.
r : RootResults (present if ``full_output = True``)
Object containing information about the convergence. In particular,
``r.converged`` is True if the routine converged.
See Also
--------
multivariate local optimizers
`fmin`, `fmin_powell`, `fmin_cg`, `fmin_bfgs`, `fmin_ncg`
nonlinear least squares minimizer
`leastsq`
constrained multivariate optimizers
`fmin_l_bfgs_b`, `fmin_tnc`, `fmin_cobyla`
global optimizers
`basinhopping`, `brute`, `differential_evolution`
local scalar minimizers
`fminbound`, `brent`, `golden`, `bracket`
n-dimensional root-finding
`fsolve`
one-dimensional root-finding
`brenth`, `ridder`, `bisect`, `newton`
scalar fixed-point finder
`fixed_point`
Notes
-----
`f` must be continuous. f(a) and f(b) must have opposite signs.
Examples
--------
>>> def f(x):
... return (x**2 - 1)
>>> from scipy import optimize
>>> root = optimize.brentq(f, -2, 0)
>>> root
-1.0
>>> root = optimize.brentq(f, 0, 2)
>>> root
1.0
References
----------
.. [Brent1973]
Brent, R. P.,
*Algorithms for Minimization Without Derivatives*.
Englewood Cliffs, NJ: Prentice-Hall, 1973. Ch. 3-4.
.. [PressEtal1992]
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.
*Numerical Recipes in FORTRAN: The Art of Scientific Computing*, 2nd ed.
Cambridge, England: Cambridge University Press, pp. 352-355, 1992.
Section 9.3: "Van Wijngaarden-Dekker-Brent Method."
"""
if not isinstance(args, tuple):
args = (args,)
if xtol <= 0:
raise ValueError("xtol too small (%g <= 0)" % xtol)
if rtol < _rtol:
raise ValueError("rtol too small (%g < %g)" % (rtol, _rtol))
r = _zeros._brentq(f,a,b,xtol,rtol,maxiter,args,full_output,disp)
return results_c(full_output, r)
def brenth(f, a, b, args=(),
xtol=_xtol, rtol=_rtol, maxiter=_iter,
full_output=False, disp=True):
"""Find root of f in [a,b].
A variation on the classic Brent routine to find a zero of the function f
between the arguments a and b that uses hyperbolic extrapolation instead of
inverse quadratic extrapolation. There was a paper back in the 1980's ...
f(a) and f(b) cannot have the same signs. Generally on a par with the
brent routine, but not as heavily tested. It is a safe version of the
secant method that uses hyperbolic extrapolation. The version here is by
Chuck Harris.
Parameters
----------
f : function
Python function returning a number. f must be continuous, and f(a) and
f(b) must have opposite signs.
a : number
One end of the bracketing interval [a,b].
b : number
The other end of the bracketing interval [a,b].
xtol : number, optional
The computed root ``x0`` will satisfy ``np.allclose(x, x0,
atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
parameter must be nonnegative. As with `brentq`, for nice
functions the method will often satisfy the above condition
with ``xtol/2`` and ``rtol/2``.
rtol : number, optional
The computed root ``x0`` will satisfy ``np.allclose(x, x0,
atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
parameter cannot be smaller than its default value of
``4*np.finfo(float).eps``. As with `brentq`, for nice functions
the method will often satisfy the above condition with
``xtol/2`` and ``rtol/2``.
maxiter : number, optional
if convergence is not achieved in maxiter iterations, an error is
raised. Must be >= 0.
args : tuple, optional
containing extra arguments for the function `f`.
`f` is called by ``apply(f, (x)+args)``.
full_output : bool, optional
If `full_output` is False, the root is returned. If `full_output` is
True, the return value is ``(x, r)``, where `x` is the root, and `r` is
a RootResults object.
disp : bool, optional
If True, raise RuntimeError if the algorithm didn't converge.
Returns
-------
x0 : float
Zero of `f` between `a` and `b`.
r : RootResults (present if ``full_output = True``)
Object containing information about the convergence. In particular,
``r.converged`` is True if the routine converged.
Examples
--------
>>> def f(x):
... return (x**2 - 1)
>>> from scipy import optimize
>>> root = optimize.brenth(f, -2, 0)
>>> root
-1.0
>>> root = optimize.brenth(f, 0, 2)
>>> root
1.0
See Also
--------
fmin, fmin_powell, fmin_cg,
fmin_bfgs, fmin_ncg : multivariate local optimizers
leastsq : nonlinear least squares minimizer
fmin_l_bfgs_b, fmin_tnc, fmin_cobyla : constrained multivariate optimizers
basinhopping, differential_evolution, brute : global optimizers
fminbound, brent, golden, bracket : local scalar minimizers
fsolve : n-dimensional root-finding
brentq, brenth, ridder, bisect, newton : one-dimensional root-finding
fixed_point : scalar fixed-point finder
"""
if not isinstance(args, tuple):
args = (args,)
if xtol <= 0:
raise ValueError("xtol too small (%g <= 0)" % xtol)
if rtol < _rtol:
raise ValueError("rtol too small (%g < %g)" % (rtol, _rtol))
r = _zeros._brenth(f,a, b, xtol, rtol, maxiter, args, full_output, disp)
return results_c(full_output, r)
| 21,346 | 33.823817 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_trustregion_constr/canonical_constraint.py
|
import numpy as np
import scipy.sparse as sps
class CanonicalConstraint(object):
"""Canonical constraint to use with trust-constr algorithm.
It represents the set of constraints of the form::
f_eq(x) = 0
f_ineq(x) <= 0
Where ``f_eq`` and ``f_ineq`` are evaluated by a single function, see
below.
The class is supposed to be instantiated by factory methods, which
should prepare the parameters listed below.
Parameters
----------
n_eq, n_ineq : int
Number of equality and inequality constraints respectively.
fun : callable
Function defining the constraints. The signature is
``fun(x) -> c_eq, c_ineq``, where ``c_eq`` is ndarray with `n_eq`
components and ``c_ineq`` is ndarray with `n_ineq` components.
jac : callable
Function to evaluate the Jacobian of the constraint. The signature
is ``jac(x) -> J_eq, J_ineq``, where ``J_eq`` and ``J_ineq`` are
either ndarray of csr_matrix of shapes (n_eq, n) and (n_ineq, n)
respectively.
hess : callable
Function to evaluate the Hessian of the constraints multiplied
by Lagrange multipliers, that is
``dot(f_eq, v_eq) + dot(f_ineq, v_ineq)``. The signature is
``hess(x, v_eq, v_ineq) -> H``, where ``H`` has an implied
shape (n, n) and provide a matrix-vector product operation
``H.dot(p)``.
keep_feasible : ndarray, shape (n_ineq,)
Mask indicating which inequality constraints should be kept feasible.
"""
def __init__(self, n_eq, n_ineq, fun, jac, hess, keep_feasible):
self.n_eq = n_eq
self.n_ineq = n_ineq
self.fun = fun
self.jac = jac
self.hess = hess
self.keep_feasible = keep_feasible
@classmethod
def from_PreparedConstraint(cls, constraint):
"""Create an instance from `PreparedConstrained` object."""
lb, ub = constraint.bounds
cfun = constraint.fun
keep_feasible = constraint.keep_feasible
if np.all(lb == -np.inf) and np.all(ub == np.inf):
return cls.empty(cfun.n)
if np.all(lb == -np.inf) and np.all(ub == np.inf):
return cls.empty(cfun.n)
elif np.all(lb == ub):
return cls._equal_to_canonical(cfun, lb)
elif np.all(lb == -np.inf):
return cls._less_to_canonical(cfun, ub, keep_feasible)
elif np.all(ub == np.inf):
return cls._greater_to_canonical(cfun, lb, keep_feasible)
else:
return cls._interval_to_canonical(cfun, lb, ub, keep_feasible)
@classmethod
def empty(cls, n):
"""Create an "empty" instance.
This "empty" instance is required to allow working with unconstrained
problems as if they have some constraints.
"""
empty_fun = np.empty(0)
empty_jac = np.empty((0, n))
empty_hess = sps.csr_matrix((n, n))
def fun(x):
return empty_fun, empty_fun
def jac(x):
return empty_jac, empty_jac
def hess(x, v_eq, v_ineq):
return empty_hess
return cls(0, 0, fun, jac, hess, np.empty(0))
@classmethod
def concatenate(cls, canonical_constraints, sparse_jacobian):
"""Concatenate multiple `CanonicalConstraint` into one.
`sparse_jacobian` (bool) determines the Jacobian format of the
concatenated constraint. Note that items in `canonical_constraints`
must have their Jacobians in the same format.
"""
def fun(x):
eq_all = []
ineq_all = []
for c in canonical_constraints:
eq, ineq = c.fun(x)
eq_all.append(eq)
ineq_all.append(ineq)
return np.hstack(eq_all), np.hstack(ineq_all)
if sparse_jacobian:
vstack = sps.vstack
else:
vstack = np.vstack
def jac(x):
eq_all = []
ineq_all = []
for c in canonical_constraints:
eq, ineq = c.jac(x)
eq_all.append(eq)
ineq_all.append(ineq)
return vstack(eq_all), vstack(ineq_all)
def hess(x, v_eq, v_ineq):
hess_all = []
index_eq = 0
index_ineq = 0
for c in canonical_constraints:
vc_eq = v_eq[index_eq:index_eq + c.n_eq]
vc_ineq = v_ineq[index_ineq:index_ineq + c.n_ineq]
hess_all.append(c.hess(x, vc_eq, vc_ineq))
index_eq += c.n_eq
index_ineq += c.n_ineq
def matvec(p):
result = np.zeros_like(p)
for h in hess_all:
result += h.dot(p)
return result
n = x.shape[0]
return sps.linalg.LinearOperator((n, n), matvec, dtype=float)
n_eq = sum(c.n_eq for c in canonical_constraints)
n_ineq = sum(c.n_ineq for c in canonical_constraints)
keep_feasible = np.array(np.hstack((
c.keep_feasible for c in canonical_constraints)), dtype=bool)
return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
@classmethod
def _equal_to_canonical(cls, cfun, value):
empty_fun = np.empty(0)
n = cfun.n
n_eq = value.shape[0]
n_ineq = 0
keep_feasible = np.empty(0, dtype=bool)
if cfun.sparse_jacobian:
empty_jac = sps.csr_matrix((0, n))
else:
empty_jac = np.empty((0, n))
def fun(x):
return cfun.fun(x) - value, empty_fun
def jac(x):
return cfun.jac(x), empty_jac
def hess(x, v_eq, v_ineq):
return cfun.hess(x, v_eq)
empty_fun = np.empty(0)
n = cfun.n
if cfun.sparse_jacobian:
empty_jac = sps.csr_matrix((0, n))
else:
empty_jac = np.empty((0, n))
return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
@classmethod
def _less_to_canonical(cls, cfun, ub, keep_feasible):
empty_fun = np.empty(0)
n = cfun.n
if cfun.sparse_jacobian:
empty_jac = sps.csr_matrix((0, n))
else:
empty_jac = np.empty((0, n))
finite_ub = ub < np.inf
n_eq = 0
n_ineq = np.sum(finite_ub)
if np.all(finite_ub):
def fun(x):
return empty_fun, cfun.fun(x) - ub
def jac(x):
return empty_jac, cfun.jac(x)
def hess(x, v_eq, v_ineq):
return cfun.hess(x, v_ineq)
else:
finite_ub = np.nonzero(finite_ub)[0]
keep_feasible = keep_feasible[finite_ub]
ub = ub[finite_ub]
def fun(x):
return empty_fun, cfun.fun(x)[finite_ub] - ub
def jac(x):
return empty_jac, cfun.jac(x)[finite_ub]
def hess(x, v_eq, v_ineq):
v = np.zeros(cfun.m)
v[finite_ub] = v_ineq
return cfun.hess(x, v)
return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
@classmethod
def _greater_to_canonical(cls, cfun, lb, keep_feasible):
empty_fun = np.empty(0)
n = cfun.n
if cfun.sparse_jacobian:
empty_jac = sps.csr_matrix((0, n))
else:
empty_jac = np.empty((0, n))
finite_lb = lb > -np.inf
n_eq = 0
n_ineq = np.sum(finite_lb)
if np.all(finite_lb):
def fun(x):
return empty_fun, lb - cfun.fun(x)
def jac(x):
return empty_jac, -cfun.jac(x)
def hess(x, v_eq, v_ineq):
return cfun.hess(x, -v_ineq)
else:
finite_lb = np.nonzero(finite_lb)[0]
keep_feasible = keep_feasible[finite_lb]
lb = lb[finite_lb]
def fun(x):
return empty_fun, lb - cfun.fun(x)[finite_lb]
def jac(x):
return empty_jac, -cfun.jac(x)[finite_lb]
def hess(x, v_eq, v_ineq):
v = np.zeros(cfun.m)
v[finite_lb] = -v_ineq
return cfun.hess(x, v)
return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
@classmethod
def _interval_to_canonical(cls, cfun, lb, ub, keep_feasible):
lb_inf = lb == -np.inf
ub_inf = ub == np.inf
equal = lb == ub
less = lb_inf & ~ub_inf
greater = ub_inf & ~lb_inf
interval = ~equal & ~lb_inf & ~ub_inf
equal = np.nonzero(equal)[0]
less = np.nonzero(less)[0]
greater = np.nonzero(greater)[0]
interval = np.nonzero(interval)[0]
n_less = less.shape[0]
n_greater = greater.shape[0]
n_interval = interval.shape[0]
n_ineq = n_less + n_greater + 2 * n_interval
n_eq = equal.shape[0]
keep_feasible = np.hstack((keep_feasible[less],
keep_feasible[greater],
keep_feasible[interval],
keep_feasible[interval]))
def fun(x):
f = cfun.fun(x)
eq = f[equal] - lb[equal]
le = f[less] - ub[less]
ge = lb[greater] - f[greater]
il = f[interval] - ub[interval]
ig = lb[interval] - f[interval]
return eq, np.hstack((le, ge, il, ig))
def jac(x):
J = cfun.jac(x)
eq = J[equal]
le = J[less]
ge = -J[greater]
il = J[interval]
ig = -il
if sps.issparse(J):
ineq = sps.vstack((le, ge, il, ig))
else:
ineq = np.vstack((le, ge, il, ig))
return eq, ineq
def hess(x, v_eq, v_ineq):
n_start = 0
v_l = v_ineq[n_start:n_start + n_less]
n_start += n_less
v_g = v_ineq[n_start:n_start + n_greater]
n_start += n_greater
v_il = v_ineq[n_start:n_start + n_interval]
n_start += n_interval
v_ig = v_ineq[n_start:n_start + n_interval]
v = np.zeros_like(lb)
v[equal] = v_eq
v[less] = v_l
v[greater] = -v_g
v[interval] = v_il - v_ig
return cfun.hess(x, v)
return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
def initial_constraints_as_canonical(n, prepared_constraints, sparse_jacobian):
"""Convert initial values of the constraints to the canonical format.
The purpose to avoid one additional call to the constraints at the initial
point. It takes saved values in `PreparedConstraint`, modify and
concatenate them to the the canonical constraint format.
"""
c_eq = []
c_ineq = []
J_eq = []
J_ineq = []
for c in prepared_constraints:
f = c.fun.f
J = c.fun.J
lb, ub = c.bounds
if np.all(lb == ub):
c_eq.append(f - lb)
J_eq.append(J)
elif np.all(lb == -np.inf):
finite_ub = ub < np.inf
c_ineq.append(f[finite_ub] - ub[finite_ub])
J_ineq.append(J[finite_ub])
elif np.all(ub == np.inf):
finite_lb = lb > -np.inf
c_ineq.append(lb[finite_lb] - f[finite_lb])
J_ineq.append(-J[finite_lb])
else:
lb_inf = lb == -np.inf
ub_inf = ub == np.inf
equal = lb == ub
less = lb_inf & ~ub_inf
greater = ub_inf & ~lb_inf
interval = ~equal & ~lb_inf & ~ub_inf
c_eq.append(f[equal] - lb[equal])
c_ineq.append(f[less] - ub[less])
c_ineq.append(lb[greater] - f[greater])
c_ineq.append(f[interval] - ub[interval])
c_ineq.append(lb[interval] - f[interval])
J_eq.append(J[equal])
J_ineq.append(J[less])
J_ineq.append(-J[greater])
J_ineq.append(J[interval])
J_ineq.append(-J[interval])
c_eq = np.hstack(c_eq) if c_eq else np.empty(0)
c_ineq = np.hstack(c_ineq) if c_ineq else np.empty(0)
if sparse_jacobian:
vstack = sps.vstack
empty = sps.csr_matrix((0, n))
else:
vstack = np.vstack
empty = np.empty((0, n))
J_eq = vstack(J_eq) if J_eq else empty
J_ineq = vstack(J_ineq) if J_ineq else empty
return c_eq, c_ineq, J_eq, J_ineq
| 12,519 | 30.938776 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/scipy/optimize/_trustregion_constr/setup.py
|
from __future__ import division, print_function, absolute_import
def configuration(parent_package='', top_path=None):
from numpy.distutils.misc_util import Configuration
config = Configuration('_trustregion_constr', parent_package, top_path)
config.add_data_dir('tests')
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())
| 424 | 29.357143 | 75 |
py
|
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